Handbook of Dynamical Systems

Volume 1B

Edited by

  • A. Katok, The Pennsylvania State University, University Park, USA
  • B. Hasselblatt, Tufts University, Department of Mathematics, Medford, MA USA

This second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey “Principal Structures” of Volume 1A.The present volume contains surveys on subjects in four areas of dynamical systems: Hyperbolic dynamics, parabolic dynamics, ergodic theory and infinite-dimensional dynamical systems (partial differential equations).
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Book information

  • Published: November 2005
  • Imprint: ELSEVIER
  • ISBN: 978-0-444-52055-5

Table of Contents

PrefaceList of ContributorsContents of Volume 1A1. Partially Hyperbolic Dynamical Systems (B. Hasselblatt and Ya. Pesin)2. Smooth Ergodic Theory and Nonuniformly Hypoerbolic Dynamics (L. Barreira and Ya. Pesin, with an Appendix by O. Sarig)3. Stochastic-Like Behaviour in Nonuniformly Expanding Maps (S. Luzzatto)4. Homoclinic Bifurcations, Dominated Splitting, and Robust Transivity (E.R. Pujals and M. Sambarino)5. Random Dynamics (Yu. Kifer, P.-D. Liu)6. An Introduction to Veech Surfaces (P. Hubert and T.A. Schmidt)7. Ergodic Theory of Translation Surfaces (H. Masur)8. On the Lyapunov Exponents of the Kontsevich-Zorich Cocycle (G. Forni)9. Counting Problems in Moduli Space (A. Eskin)10. On the Interplay Between Measurable and Topological Dynamics (E. Glasner and B. Weiss)11. Spectral Properties and Combinatorial Constructions in Ergodic Theory (A. Katok and J.-P. Thouvenot)12. Combinatorial and Diophantine Applications of Ergodic Theory (V. Bergelson, with Appendix A by A. Leibman and Appendix B by A. Quas and M. Wierdl)13. Pointwise Ergodic Theorems for Actions of Groups (A. Nevo)14. Global Attractors in PDE (A.V. Babin)15. Hamiltonian PDEs (S.B. Kuksin, with an Appendix by D. Bambusi)16. Extended Hamiltonian Systems (M.I. Weinstein)Author Index of Volume 1ASubject Index of Volume 1AAuthor IndexSubject Index