Modern Dynamical Systems and Applications

This volume presents a broad collection of current research by leading experts in the theory of dynamical systems.

Michael Brin (Edited by), Boris Hasselblatt (Edited by), Yakov Pesin (Edited by)

9780521840736, Cambridge University Press

Hardback, published 16 August 2004

474 pages
26.2 x 18.8 x 3.8 cm, 1.035 kg

This volume presents a wide cross section of current research in the theory of dynamical systems and contains articles by leading researchers, including several Fields medalists, in a variety of specialties. These are surveys, usually with new results included, as well as research papers that are included because of their potentially high impact. Major areas covered include hyperbolic dynamics, elliptic dynamics, mechanics, geometry, ergodic theory, group actions, rigidity, applications. The target audience includes dynamicists, who will find new results in their own specialty as well as surveys in others, and mathematicians from other disciplines who look for a sample of current developments in ergodic theory and dynamical systems.

1. Introduction Michael Brin, Boris Hasselblatt and Yakov Pesin
Part I. Ergodic Theory, Rigidity, Geometry: 2. Weakly mixing actions of general groups: a brief survey and an example Vitaly Bergelson and Alex Gorodnik
3. Dynamical Morse entropy Melanie Bertelson and Michael Gromov
4. Positive k-theory and symbolic dynamics Michael Boyle and Jack Wagoner
5. Geometry of 2-step nilpotent Lie groups with a left invariant metric Patrick Eberlein
6. A differential-geometric view of normal forms of contractions Renato Feres
7. Averaging along cubes B. Host and Bryna Kra
8. Sections for semiflows and Kakutani shift equivalence Chao-Hui Lin and Daniel Rudolph
9. Coarsely geodesic metrics on reductive groups Herbert Abels and Gregory Margulis
10. Algebraic Zd-actions on zero-dimensional compact Abelian groups Klaus Schmidt
11. An invitation to rigidity theory Ralf Spatzier
12. Remarks on magnetic flows and magnetic billiards, Finsler metrics and a magnetic analog of Hilbert's fourth problem Serge Tabachnikov
Part II. Hyperbolic Dynamics: 13. Expanding polymodials Alexander Blokh, Chris Cleveland and Michal Misiurewicz
14. Lyapunov exponents: how frequently are dynamical systems hyperbolic? Jairo Bochi and Marcelo Viana
15. A Hölder continuous vector field tangent to many foliations Christina Bonatti and John Franks
16. On partially hyperbolic diffeomorphisms of 3-manifolds with commutative fundamental groups Michael Brin, Dmitri Burago and S. Ivanov
17. Prelude to a kiss Dmitry Dolgopyat
18. Nonuniform hpyerbolicity and elliptic dynamics Bassam Fayad
19. Dimension product structure of hyperbolic sets Boris Hasselblatt and Jorg Schmeling
20. Every compact manifold carries a hyperbolic Bernoulli flow Huyi Hu, Yakov Pesin and Anna Talitskaya
21. Parameter choice for families of maps with many critical points Michael Jakobson
22. Entropy, exponents and invariant densities for hyperbolic systems: dependence and computation Oliver Jenkinson and Mark Pollicott
23. Some recent advances in averaging Yuri Kifer
24. Bootstrap of regularity for integrable solutions of cohomology equations Rafael de la Llave
25. Cone-fields, domination, and hyperbolicity Sheldon Newhouse
26. Markov towers and stochastic properties of billiards Domokos Szasz and Tamas Varju
27. Some questions and remarks about SL(2,R) cocycles Jean-Christophe Yoccoz.

Subject Areas: Nonlinear science [PBWR], Applied mathematics [PBW], Differential calculus & equations [PBKJ]