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Headline

This is a section of the Basic Math Library List


  • Please help improve the article.


  • The books taged by HK are highlited in [HK]. Most of them recommended.
  • The books taged by MR has received very positive reviews in Mathscinet, though some of them are not relevant for the basic library list.



10. Dynamical systems and ordinary differential equations 
    Topological and symbolic dynamics. Geometric and qualitative theory of ODE and smooth dynamical systems,
    bifurcations and singularities. Hamiltonian systems and dynamical systems of geometric origin.
    One-dimensional and holomorphic dynamics. Multidimensional actions and rigidity in dynamics.
    Ergodic theory including applications to combinatorics and combinatorial number theory.
    Connections with sections  5, 7, 8, 9, 11, 12, 13, 14, 16, 17.

  • To add books by: Marcarian Chernov, Palis Takens, ...

Books providing a broad coverage

Anatole Katok and Boris Hasselblatt, Introduction to the modern theory of dynamical systems, Cambridge, 1996, ISBN 0-521-57557-5 recommended


Christian Bonatti, Lorenzo J. Díaz, Marcelo Viana, Dynamics Beyond Uniform Hyperbolicity: A Global Geometric and Probabilistic Perspective, Springer, 2005, ISBN 3-540-22066-6 recommended


Encyclopaedia of Mathematical Sciences (ISSN 0938-0396) has a sub-series on dynamical systems with reviews of current research.


Diederich Hinrichsen and Anthony J. Pritchard, Mathematical Systems Theory I - Modelling, State Space Analysis, Stability and Robustness, Springer Verlag, 2005, ISBN 978-3-540-44125-0


Mikhail Lyubich, John W. Milnor and Yair N. Minsky (Editors), Laminations and foliations in dynamics, geometry and topology. Proceedings of the conference held at SUNY, Stony Brook, NY, May 18--24, 1998. Contemporary Mathematics, 269. American Mathematical Society, Providence, RI, 2001. xii+233 pp. ISBN 0-8218-1985-2 MR1810533 (2001h:00027) 00B25 (32-06 57-06)


Bodil Branner, Poul Hjorth (Editors), Real and Complex Dynamical Systems: Proceedings of the NATO ASI, Hillerod, Denmark, June 20 - July 2, 1993, North Atlantic Treaty Organization Scientific Affairs Division Contributor Bodil Branner, Poul Hjorth Published by Springer, 1995 ISBN 079233521X, ISBN 9780792335214 recommended --surveys and expositions on some topics in Real and complex dynamics, including a nice paper by J C Yoccoz on "introduction on hyperbolic dynamics".


Anatole Katok and Boris Hasselblatt (Ed.), Handbooks Dynamical systems, Bifurcations, Handbooks in Mathematics, Elsevier, 3 volumes KH recommended


Introductory books

Jacob Palis and Wellington de Melo, Geometric theory of dynamical systems: an introduction, Springer-Verlag, 1982, ISBN 0-387-90668-1 recommended


David Ruelle, Elements of Differentiable Dynamics and Bifurcation Theory, Academic Press, 1989, ISBN 0-12-601710-7


Brin, Michael; Stuck, Garrett, Introduction to dynamical systems. Cambridge University Press, Cambridge, 2002. xii+240 pp. ISBN: 0-521-80841-3 recommended


Hasselblatt, Boris; Katok, Anatole, A first course in dynamics. With a panorama of recent developments. Cambridge University Press, New York, 2003. x+424 pp. \$95.00; \$35.00 paperbound. ISBN 0-521-58304-7; 0-521-58750-6 KH


Steven Strogatz, Nonlinear dynamics and chaos: with applications to physics, biology chemistry and engineering, Addison Wesley, year= 1994,ISBN 0-201-54344-3


Kathleen T. Alligood, Tim D. Sauer and James A. Yorke, Chaos. An introduction to dynamical systems, Springer Verlag, 2000, ISBN 0-387-94677-2


Morris W. Hirsch, Stephen Smale and Robert Devaney, Differential Equations, dynamical systems, and an introduction to chaos, Academic Press, 2003, ISBN 0-12-349703-5 recommended


Perko, Lawrence, Differential equations and dynamical systems. Third edition. Texts in Applied Mathematics, 7. Springer-Verlag, New York, 2001. xiv+553 pp. \$69.95. ISBN 0-387-95116-4 recommended


Ralph Abraham and Christopher D. Shaw, Dynamics - the geometry of behavior, 2nd edition, Addison-Wesley, 1992, ISBN= 0-201-56716-4


Clark Robinson, Dynamical systems. Stability, symbolic dynamics and chaos, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995 KH recommended


Topological and Smooth Dynamics

William Parry, Mark Pollicott, Zeta functions and periodic orbit structure of hyperbolic dynamics, Asterisque 187–188, Societe Mathematique de France, Paris, 1990 KH


Klaus Schmidt, Dynamical systems of algebraic origin, Progress in Mathematics 128, Birkhauser Verlag, Basel, Boston, 1995 KH


Douglas Lind, Lawrence Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, 1995 KH


Natasha Jonoska, Subshifts of Finite Type, Sofic Systems and Graphs, (2000).


Mahendra G. Nadkarni, Spectral theory of dynamical systems, Birkhauser Advanced Texts, Basler Lehrbucher. Birkhauser Verlag, Basel, 1998 KH


Birkhoff, George David, Dynamical systems, Colloquium Publications 9, American Mathematical Society, Providence, RI, 1927 KH


Alongi, John M.; Nelson, Gail S. Recurrence and topology. Graduate Studies in Mathematics, 85. American Mathematical Society, Providence, RI, 2007. x+221 pp. ISBN 978-0-8218-4234-8; 0-8218-4234-X (Reviewer: Michael Hurley) 37B20 (34D45 37-01 37B25 54H20) MR2330357 (2008i:37023) MR


Vladimir M. Alekseev, Quasirandom dynamical systems. I. Quasirandom diffeomorphisms, Mat. Sb. (N.S.) 76 (118) (1968), 72–134; Invariant Markov subsets of diffeomorphisms, Uspehi Mat. Nauk 23 (1968), no. 2 (140) 209–210 KH 2 Papers


Morris, Dave Witte, Ratner's theorems on unipotent flows. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 2005. xii+203 pp. ISBN 0-226-53983-0; 0-226-53984-9 (Reviewer: Bachir Bekka) 37A17 (22E40 22F30 37A25 37A30 37A35) MR2158954 (2006h:37006) MR


Feudel, Ulrike; Kuznetsov, Sergey; Pikovsky, Arkady, Strange nonchaotic attractors. Dynamics between order and chaos in quasiperiodically forced systems. World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, 56. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006. xii+213 pp. ISBN 981-256-633-3 (Reviewer: Peter Ashwin) 37C55 (37D99 37E20 70K99) MR2261529 (2007j:37039) MR


Kechris, Alexander S.; Miller, Benjamin D., Topics in orbit equivalence. Lecture Notes in Mathematics, 1852. Springer-Verlag, Berlin, 2004. x+134 pp. ISBN 3-540-22603-6 (Reviewer: Bachir Bekka) 37A15 (03E15 28D15 37A20) MR2095154 (2005f:37010) MR


The theory of chaotic attractors. Dedicated to James A. Yorke in commemoration of his 60th birthday. Edited by Brian R. Hunt, Judy A. Kennedy, Tien-Yien Li and Helena E. Nusse. Springer-Verlag, New York, 2004. x+514 pp. ISBN 0-387-40349-3 37-06 (00B30 34-06 34C28 37D45) MR2042540 (2005b:37004) MR


Manneville, Paul, Instabilities, chaos and turbulence. An introduction to nonlinear dynamics and complex systems. Imperial College Press, London, 2004. xiv+391 pp. ISBN 1-86094-483-3 (Reviewer: Athanasios Yannacopoulos) 37N10 (37D45 76E30 76F20) MR2155902 (2006g:37136) MR


Mora, Leonardo; Romero, Neptalí Introducción a los sistemas dinámicos vía la aplicación de Henón. (Spanish) [Introduction to dynamical systems via the Hénon map] Monografías del Instituto de Matemática y Ciencias Afines [Monographs of the Institute of Mathematics and Related Sciences], 14. Instituto de Matemática y Ciencias Afines, IMCA, Lima; Pontificia Universidad Católica del Perú, Lima, 2000. viii+80 pp. ISBN 9972-753-53-0 (Reviewer: André Salles de Carvalho) 37-01 (37E30) MR2008868 (2004k:37001) MR


Wiggins, Stephen, Introduction to applied nonlinear dynamical systems and chaos. Second edition. Texts in Applied Mathematics, 2. Springer-Verlag, New York, 2003. xxx+843 pp. ISBN 0-387-00177-8 (Reviewer: Carmen Chicone) 37-01 (34-01 34C28 37D45 70K50 70K55) MR2004534 (2004h:37002) MR


Palmer, Ken, Shadowing in dynamical systems. Theory and applications. Mathematics and its Applications, 501. Kluwer Academic Publishers, Dordrecht, 2000. xiv+299 pp. ISBN 0-7923-6179-2 (Reviewer: S. Yu. Pilyugin) 37C50 (34C37 34D09 37C20 37C29 37D05) MR1885537 (2002k:37034) MR


Elaydi, Saber N., Discrete chaos. Chapman & Hall/CRC, Boca Raton, FL, 2000. xiv+355 pp. ISBN 1-58488-002-3 37-01 (37D45 37Exx) MR1737407 (2002b:37001) MR


One-dimensional and Holomorphic Dynamics

Welington de Melo, Sebastian van Strien, One-dimensional dynamics, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 25. Springer-Verlag, Berlin-New York, 1993 KH


Lluis Alseda, Jaume Llibre, Michal Misiurewicz, Combinatorial dynamics and entropy in dimension one, Advanced Series in Nonlinear Dynamics, 5. World Scientific Publishing Co., Inc., River Edge, NJ, 1993 KH


Carleson, Lennart; Gamelin, Theodore W., Complex dynamics. Universitext: Tracts in Mathematics. Springer-Verlag, New York, 1993. x+175 pp. ISBN 0-387-97942-5 KH


Beardon, Alan F., Iteration of rational functions. Complex analytic dynamical systems. Graduate Texts in Mathematics, 132. Springer-Verlag, New York, 1991. xvi+280 pp. ISBN 0-387-97589-6


Milnor, John Dynamics in one complex variable. Introductory lectures. Friedr. Vieweg & Sohn, Braunschweig, 1999. viii+257 pp. ISBN 3-528-03130-1 (Reviewer: Dierk Schleicher) 37Fxx (30D05 37-01) MR1721240 (2002i:37057) recommended MR -- online


Berteloot, François; Mayer, Volker Rudiments de dynamique holomorphe. (French) [Rudiments of holomorphic dynamics] Cours Spécialisés [Specialized Courses], 7. Société Mathématique de France, Paris; EDP Sciences, Les Ulis, 2001. vi+160 pp. ISBN 2-86883-521-X (Reviewer: Mattias Jonsson) 37F10 (30D05 32H50 37-01 37F15 37F50 39B12) MR1973050 (2005b:37087) MR


de Faria, Edson; de Melo, Welington One dimensional dynamics. The mathematical tools. Publicações Matemáticas do IMPA. [IMPA Mathematical Publications] 23$\sp {\rm o}$ Colóquio Brasileiro de Matemática. [23rd Brazilian Mathematics Colloquium] Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2001. ii+100 pp. ISBN 85-244-0179-6 (Reviewer: Saeed Zakeri) 37Fxx (30C62 30D05 30F10 37-02) MR1851555 (2002f:37077) MR recommended



Ergodic Theory

Mañé, Ricardo, Ergodic theory and differentiable dynamics. Translated from the Portuguese by Silvio Levy. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 8. Springer-Verlag, Berlin, 1987. xii+317 pp. \$82.00. ISBN 3-540-15278-4 KH recommended


Walters, Peter, An introduction to ergodic theory. Graduate Texts in Mathematics, 79. Springer-Verlag, New York-Berlin, 1982. ix+250 pp. \$28.00. ISBN 0-387-90599-5 KH recommended


Pollicott, Mark, Lectures on ergodic theory and Pesin theory on compact manifolds. (English. English summary) London Mathematical Society Lecture Note Series, 180. Cambridge University Press, Cambridge, 1993. x+162 pp. \$37.95. ISBN 0-521-43593-5


Pollicott, Mark; Yuri, Michiko, Dynamical systems and ergodic theory. (English. English summary) London Mathematical Society Student Texts, 40. Cambridge University Press, Cambridge, 1998. xiv+179 pp. \$59.95; \$22.95 paperbound. ISBN 0-521-57294-0; 0-521-57599-0


Tim Bedford, Michael Keane and Caroline Series, eds., Ergodic theory, symbolic dynamics and hyperbolic spaces, Oxford University Press, 1991, ISBN 0-19-853390-X


Karl Petersen, Ergodic Theory (Cambridge Studies in Advanced Mathematics). Cambridge: Cambridge University Press. 1990. KH recommended


Karl E. Petersen and Ibrahim A. Salama, (eds.), Ergodic Theory and its Connections with Harmonic Analysis, Proceedings of the 1993 Alexandria Conference, (1995)Cambridge University Press, Cambridge, ISBN 0-521-45999-0.


Donald Ornstein, Ergodic theory, randomness, and dynamical systems, James K. Whittemore Lectures in Mathematics given at Yale University. Yale Mathematical Monographs 5. Yale University Press, New Haven, CT-London, 1974 KH


William Parry, Entropy and generators in ergodic theory, W. A. Benjamin, Inc., New York–Amsterdam, 1969 KH


William Parry, Topics in ergodic theory, Cambridge tracts in Mathematics, 75. Cambridge University Press, 1981 KH


David Ruelle, Thermodynamic formalism, The mathematical structure of classical equilibrium statistical mechanics, Encyclopedia of Mathematics and its Applications, 5. Addison-Wesley Publishing Co., Reading, MA, 1978 KH


David Ruelle, Statistical mechanics, Rigorous results, W. A. Benjamin, Inc., New York-Amsterdam, 1969 KH


Robert Zimmer, Ergodic theory and semisimple groups, Monographs in Mathematics, 81. Birkhauser Verlag, Basel-Boston, MA, 1984 KH


Ulrich Krengel, Ergodic theorems, de Gruyter Studies in Mathematics, 6. Walter de Gruyter & Co., Berlin-New York, 1985 KH


Hillel Furstenberg, Recurrence in ergodic theory and combinatorial number theory, Princeton University Press 1981 KH recommended


Paul R. Halmos, Lectures on ergodic theory, Chelsea Publishing Co., New York, 1960 KH


Luis Barreira, Anatole Katok, Yakov Pesin, Nonuniformly hyperbolic dynamical systems, ???? KH


Rufus Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Springer Lecture Notes in Mathematics 470, 1975 KH -- new version to appear, online?


Isaak P. Cornfeld, Sergei V. Fomin, Yakov G. Sinai, Ergodic theory, Grundlehren der mathematischen Wissenschaften 245, Springer-Verlag, 1982 KH


Dajani, Karma; Kraaikamp, Cor, Ergodic theory of numbers. Carus Mathematical Monographs, 29. Mathematical Association of America, Washington, DC, 2002. x+190 pp. ISBN 0-88385-034-6 (Reviewer: Thomas Ward) 37A45 (11K50 11K55 11K60 28D05) MR1917322 (2003f:37014) MR


Bekka, M. Bachir; Mayer, Matthias, Ergodic theory and topological dynamics of group actions on homogeneous spaces. London Mathematical Society Lecture Note Series, 269. Cambridge University Press, Cambridge, 2000. x+200 pp. ISBN 0-521-66030-0 (Reviewer: S. G. Dani) 37A15 (11E99 22E40 22F30 37A30 37C85) MR1781937 (2002c:37002) MR


MR2128542 (2005k:37002) Zaharopol, Radu Invariant probabilities of Markov-Feller operators and their supports. Frontiers in Mathematics. Birkhäuser Verlag, Basel, 2005. xiv+108 pp. ISBN 3-7643-7134-X; 978-3-7643-7134-0 (Reviewer: Onésimo Hernández Lerma) 37-02 (00-02 28D05 37A30 47A35 60J05) MR


Glasner, Eli, Ergodic theory via joinings. Mathematical Surveys and Monographs, 101. American Mathematical Society, Providence, RI, 2003. xii+384 pp. ISBN 0-8218-3372-3 (Reviewer: Andrés del Junco) 37A15 (28Dxx 37A25 37A35 37A45 37B99 54H20) MR1958753 (2004c:37011) MR


MR1920023 (2004c:37057) Simiu, Emil Chaotic transitions in deterministic and stochastic dynamical systems. Applications of Melnikov processes in engineering, physics, and neuroscience. Princeton Series in Applied Mathematics. Princeton University Press, Princeton, NJ, 2002. xiv+224 pp. ISBN 0-691-05094-5 (Reviewer: Peter E. Kloeden) 37D45 (37H20 82C05 92C20) MR


MR1862379 (2003a:37040) Barreira, Luis; Pesin, Yakov B. Lyapunov exponents and smooth ergodic theory. University Lecture Series, 23. American Mathematical Society, Providence, RI, 2002. xii+151 pp. ISBN 0-8218-2921-1 (Reviewer: Viviane Baladi) 37D25 (34D08 37C40 37D10) MR recommended


MR1723992 (2000m:37087) Arnold, Ludwig, Random dynamical systems. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 1998. xvi+586 pp. ISBN 3-540-63758-3 (Reviewer: Yuri Kifer) 37Hxx (37-02 60H10) MR

Yakov B. Pesin. Dimension Theory in Dynamical Systems: contemporary views and applications /,  Chicago Press,1998,  304 pp

Hamiltonian Dynamics

Vladimir Arnold, Mathematical methods of classical mechanics, Springer-Verlag, 1982, ISBN 0-387-96890-3 KH recommended


Ralph Abraham and Jerrold E. Marsden, Foundations of mechanics, Benjamin-Cummings,1978,ISBN 0-8053-0102-X (available as a reprint: ISBN 0-201-40840-6) KH


Meyer, Kenneth R.(1-CINC); Hall, Glen R.(1-BOST) Introduction to Hamiltonian dynamical systems and the $N$-body problem. Applied Mathematical Sciences, 90. Springer-Verlag, New York, 1992. xii+292 pp. \$49.80. ISBN 0-387-97637-X


Dankowicz, Harry(S-RIT), Chaotic dynamics in Hamiltonian systems. (English. English summary) With applications to celestial mechanics. World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, 25. World Scientific Publishing Co., Inc., River Edge, NJ, 1997. xiv+209 pp. \$38.00. ISBN 981-02-3221-7


Moser, Jürgen, Stable and random motions in dynamical systems. (English. English summary) With special emphasis on celestial mechanics. Reprint of the 1973 original. With a foreword by Philip J. Holmes. Princeton Landmarks in Mathematics. Princeton University Press, Princeton, NJ, 2001. xii+198 pp. \$14.95. ISBN 0-691-08910-8 KH recommended


Moulton, Forest Ray, An Introduction to Celestial Mechanics 2d rev. ed.New York, Dover Publications, 1970. xii, 436 pp. ISBN 048662563X


Golé, Christophe Symplectic twist maps. Global variational techniques. Advanced Series in Nonlinear Dynamics, 18. World Scientific Publishing Co., Inc., River Edge, NJ, 2001. xviii+305 pp. ISBN 981-02-0589-9 (Reviewer: Hansjörg Geiges) 37J10 (37E40 37E45 37J45 53D05 70H08) MR1992005 (2004f:37070) MR


Sussman, Gerald Jay; Wisdom, Jack; Mayer, Meinhard E., Structure and interpretation of classical mechanics. (English. English summary) MIT Press, Cambridge, MA, 2001. xxiv+534 pp. \$60.00. ISBN 0-262-19455-4


R. S. MacKay and J. D. Meiss. (Editors) Hamiltonian dynamical systems. Adam Hilger, Ltd., Bristol, 1987. xii+784 pp. \$43.00. ISBN 0-85274-216-9 recommended -- a collection of important papers


Hofer, Helmut(CH-ETHZ); Zehnder, Eduard(CH-ETHZ), Symplectic invariants and Hamiltonian dynamics. (English. English summary) Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks] Birkhäuser Verlag, Basel, 1994. xiv+341 pp. \$59.50. ISBN 3-7643-5066-0 KH recommended


Dmitry V. Anosov, Geodesic flows on Riemannian manifolds with negative curvature, Proceedings of the Steklov Institute of Mathematics 90 American Mathematical Society, Providence, RI, 1967 KH


Morales Ruiz, Juan J., Differential Galois theory and non-integrability of Hamiltonian systems. Progress in Mathematics, 179. Birkhäuser Verlag, Basel, 1999. xiv+167 pp. ISBN 3-7643-6078-X (Reviewer: Richard C. Churchill) 37J30 (12H05 32G34 34M99 37J10 70F07 70H07) MR1713573 (2000g:37076) MR


Haller, G. Chaos near resonance. Applied Mathematical Sciences, 138. Springer-Verlag, New York, 1999. xvi+427 pp. ISBN 0-387-98697-9 (Reviewer: Yan Guang (Charles) Li) 37-02 (34C37 35B34 35Q55 37D45 37J40 37K50 37L10) MR1714708 (2000m:37001) MR


Arnold, V. I.; Kozlov, V. V.; Neishtadt, A. I. Mathematical aspects of classical and celestial mechanics. Translated from the 1985 Russian original by A. Iacob. Reprint of the original English edition from the series Encyclopaedia of Mathematical Sciences [Dynamical systems. III, Encyclopaedia Math. Sci., 3, Springer, Berlin, 1993; MR1292465 (95d:58043a)]. Springer-Verlag, Berlin, 1997. xiv+291 pp. ISBN 3-540-61224-6 (Reviewer: Ana Nunes) 37Jxx (70Fxx 70Hxx 70Jxx 70Kxx) MR1656199 (2000b:37054) MR recommended


Hanßmann, Heinz Local and semi-local bifurcations in Hamiltonian dynamical systems. Results and examples. Lecture Notes in Mathematics, 1893. Springer-Verlag, Berlin, 2007. xvi+237 pp. ISBN 978-3-540-38894-4; 3-540-38894-X (Reviewer: Thomas Wagenknecht) 37J20 (34C23 37G15 37J40 70H08) MR2268416 (2008a:37061) MR


Roy Chowdhury, A. Lie algebraic methods in integrable systems. Chapman & Hall/CRC Research Notes in Mathematics, 415. Chapman & Hall/CRC, Boca Raton, FL, 2000. x+354 pp. ISBN 1-58488-037-6 37K30 (17B80) MR1723047 (2002b:37113) MR


MR1792190 (2002g:37071) Bolsinov, A. V.; Fomenko, A. T. {\cyr Integriruemye gamil'tonovy sistemy.} 1, 2. (Russian) [Integrable Hamiltonian systems. 1, 2] {\cyr Geometriya, topologiya, klassifikatsiya}. [Geometry, topology, classification] Appendices 2 and 3 by V. V. Kalashnikov, Jr. Izdatel'skii Dom ``Udmurt\cydot skii Universitet, Izhevsk, 1999. 1: 444 pp.; 2: 447 pp. ISBN 5-7029-0352-8 (Reviewer: Peter J. Topalov) 37J35 (53D25 70E40 70H06) MR


MR1689375 (2000h:37077) Mangiarotti, L.; Sardanashvily, G. Gauge mechanics. World Scientific Publishing Co., Inc., River Edge, NJ, 1998. x+355 pp. ISBN 981-02-3603-4 (Reviewer: Manuel de León) 37Jxx (53D17 58A20 70G45 70H03 70Sxx) MR


MR1664068 (2000g:37079) Bolsinov, A. V.; Fomenko, A. T. {\cyr Vvedenie v topologiyu integriruemykh gamil'tonovykh sistem}. (Russian) [Introduction to the topology of integrable Hamiltonian systems] {\cyr Kibernetika: Neogranichennye Vozmozhnosti i Vozmozhnye Ogranicheniya}. [Cybernetics: Unlimited Possibilities and Possible Limitations] ``Nauka, Moscow, 1997. 352 pp. ISBN 5-02-013537-2 (Reviewer: Peter J. Topalov) 37J35 (37D40 57Rxx 70H05 70H06) MR


MR2337886 (2008i:37112) Marsden, Jerrold E.; Misiolek, Gerard; Ortega, Juan-Pablo; Perlmutter, Matthew; Ratiu, Tudor S. Hamiltonian reduction by stages. Lecture Notes in Mathematics, 1913. Springer, Berlin, 2007. xvi+519 pp. ISBN 978-3-540-72469-8 (Reviewer: Oana M. Dragulete) 37J15 (37K65 53D20 70G45 70G65 70H33) MR


MR2165554 (2006h:37065) Ragazzo, Clodoaldo G.; Dias Carneiro, Mário J.; Addas Zanata, Salvador Introdução à dinâmica de aplicações do tipo twist. (Portuguese) [Introduction to twist map dynamics] Publicações Matemáticas do IMPA. [IMPA Mathematical Publications] Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2005. ii+168 pp. ISBN 85-244-0228-8 (Reviewer: Sonia Pinto de Carvalho) 37E40 (37C29 37Nxx) MR


MR2095251 (2006d:37106) Adler, Mark; van Moerbeke, Pierre; Vanhaecke, Pol Algebraic integrability, Painlevé geometry and Lie algebras. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 47. Springer-Verlag, Berlin, 2004. xii+483 pp. ISBN 3-540-22470-X (Reviewer: Emma Previato) 37J35 (14H70 14K05 17B80 53D25) MR


MR1972063 (2004g:37074) Audin, Michèle Les systèmes hamiltoniens et leur intégrabilité. (French) [Hamiltonian systems and their integrability] Cours Spécialisés [Specialized Courses], 8. Société Mathématique de France, Paris; EDP Sciences, Les Ulis, 2001. viii+170 pp. ISBN 2-86883-522-8 (Reviewer: Emma Previato) 37J35 (12H20 14H70 14P25 70H06) MR


MR2268416 (2008a:37061) Hanßmann, Heinz Local and semi-local bifurcations in Hamiltonian dynamical systems. Results and examples. Lecture Notes in Mathematics, 1893. Springer-Verlag, Berlin, 2007. xvi+237 pp. ISBN 978-3-540-38894-4; 3-540-38894-X (Reviewer: Thomas Wagenknecht) 37J20 (34C23 37G15 37J40 70H08) MR


MR1771493 (2003a:37072) Bolsinov, A. V.; Fomenko, A. T. Integrable geodesic flows on two-dimensional surfaces. Monographs in Contemporary Mathematics. Consultants Bureau, New York, 2000. xiv+322 pp. ISBN 0-306-11065-2 (Reviewer: Vladimir S. Matveev) 37J35 (37J30 53D20 53D25 70E17 70E40) MR


Applications

Meiss, James D., Differential dynamical systems. Mathematical Modeling and Computation, 14. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2007. xxii+412 pp. ISBN 978-0-898716-35-1 (Reviewer: James W. Swift) 37-01 (34-01 34C23 37C10 37J05 37Nxx) MR2384060 MR


Izhikevich, Eugene M., Dynamical systems in neuroscience: the geometry of excitability and bursting. Computational Neuroscience. MIT Press, Cambridge, MA, 2007. xvi+441 pp. ISBN 978-0-262-09043-8; 0-262-09043-0 (Reviewer: Jonathan E. Rubin) 37N25 (34C60 37C10 37G99 92C20) MR2263523 (2008b:37156) MR


Berti, Massimiliano Nonlinear oscillations of Hamiltonian PDEs. Progress in Nonlinear Differential Equations and their Applications, 74. Birkhäuser Boston, Inc., Boston, MA, 2007. xiv+180 pp. ISBN 978-0-8176-4680-6 (Reviewer: Enrico Valdinoci) 37K05 (35B05 35L70 35Q55 47J15 47N20 58E05) MR2345400 (2008i:37133) MR


Klein, Christian; Richter, Olaf, Ernst equation and Riemann surfaces. Analytical and numerical methods. Lecture Notes in Physics, 685. Springer-Verlag, Berlin, 2005. x+249 pp. ISBN 978-3-540-28589-2; 3-540-28589-X (Reviewer: Ian A. B. Strachan) 37K20 (37N20 58E50 83C05) MR2187690 (2006k:37194) MR


Deutsch, Andreas; Dormann, Sabine, Cellular automaton modeling of biological pattern formation. Characterization, applications, and analysis. With a foreword by Philip K. Maini. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston, Inc., Boston, MA, 2005. xxiv+331 pp. ISBN 0-8176-4281-1 (Reviewers: Veronica Grieneisen and Stan Marée) 37B15 (37N25 68Q80 82C32 92C15) MR2100608 (2007j:37024) MR


Gesztesy, Fritz; Holden, Helge, Soliton equations and their algebro-geometric solutions. Vol. I. $(1+1)$-dimensional continuous models. Cambridge Studies in Advanced Mathematics, 79. Cambridge University Press, Cambridge, 2003. xii+505 pp. ISBN 0-521-75307-4 (Reviewer: Emma Previato) 37K40 (14H70 34L05 35Q53 37K10 37K15 37K20) MR1992536 (2005b:37173) MR


Jackson, E. Atlee, Exploring nature's dynamics. With 1 IBM-PC floppy disk (3.5 inch, HD). Wiley Series in Nonlinear Science. Wiley-Interscience, New York, 2001. xxiv+303 pp. ISBN 0-471-19146-9 (Reviewer: Frederick R. Marotto) 37-01 (00A69 34C60 37N25 92B05) MR1829689 (2002d:37001) MR


Contopoulos, George, Order and chaos in dynamical astronomy. Astronomy and Astrophysics Library. Springer-Verlag, Berlin, 2002. xiv+624 pp. ISBN 3-540-43360-0 (Reviewer: A. Giorgilli) 37N05 (37D45 37J40 70F15 70H05 70K55 85A05) MR1988785 (2004f:37114) MR


Kulenovic, Mustafa R. S.; Merino, Orlando, Discrete dynamical systems and difference equations with $Mathematica$. Chapman & Hall/CRC, Boca Raton, FL, 2002. xvi+344 pp. ISBN 1-58488-287-5 (Reviewer: Frederick R. Marotto) 37-01 (37-04 39-01) MR1935823 (2003j:37001) MR


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Popularizations

Florin Diacu and Philip Holmes, Celestial Encounters, Princeton, 1996, ISBN 0-691-02743-9 recommended


James Gleick, Chaos: Making a New Science, Penguin, 1988, ISBN 0-14-009250-1


Ivar Ekeland, Mathematics and the Unexpected (Paperback), University Of Chicago Press, 1990, ISBN 0-226-19990-8


Ian Stewart, Does God Play Dice? The New Mathematics of Chaos, Penguin,1997, ISBN 0140256024



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