## Handbook of Dynamical Systems, Vol. 1A

#### The editors and authors dedicate this volume to Jurgen
Kurt Moser (1928-1999) and Michael Robert Herman (1942-2000), who passed
away while this book was being written. Both of them made seminal
contributions to various areas of the theory of dynamical systems as well as
to other mathematical disciplines. Their crucial influence was further
enhanced through numerous major contributions of their students and
collaborators. The deaths of Moser and Herman are tremendous losses for the
mathematical community.

### Contents

Preface.

Principal structures (B. Hasselblatt, A. Katok); pp. 1-203.

Entropy, Isomorphism and Equivalence (J.-P. Thouvenot); pp. 205-238.

Hyperbolic dynamics (B. Hasselblatt); pp. 239-319.

Invariant measures for hyperbolic dynamical systems (N. Chernov); pp. 320-407.

Periodic orbits and zeta functions (M. Pollicott); pp. 409-452.

Hyperbolic dynamics and Riemannian geometry (G. Knieper); pp. 453-545.

Topological Methods in Dynamics (J. Franks, M. Misiurewicz); pp. 547-598.

One-Dimensional Maps (M. Jakobson, G. Swiatek); pp. 599-664.

Ergodic theory and dynamics of G-spaces (R. Feres, A. Katok); pp. 665-763.

Symbolic and algebraic dynamical systems (D. Lind, K. Schmidt); pp. 765-812.

Homogeneous flows, applications to number theory, and related topics
(D. Kleinbock, N. Shah, A. Starkov); pp. 813-930.

Random transformations in ergodic theory (A. Furman); pp.931-1014.

Rational billiards and flat structures (H. Masur, S. Tabachnikov); pp. 1015-1089.

Variational methods for Hamiltonian systems (P.H. Rabinowitz); pp. 1091-1127.

Pseudoholomorphic curves and dynamics in three dimensions (H. Hofer, K. Wysocki,
E. Zehnder); pp. 1129-1188.

This volume is the first part of the two-volume set which will cover most core areas of
the modern theory of dynamical systems
The subsequent Volume 1B
will appear in November 2005.

Additional volumes of the Handbook in Dynamical Systems series cover Applications
(Volume 2, published in 2002) and Geometric Methods of Differentiable Dynamics (Volume 3,
to be published).