#54:
Dynamics, Ergodic Theory, and Geometry
Up: MSRI Publications
MSRI Publications – Volume 54
Dynamics, Ergodic Theory, and Geometry
Dedicated to Anatole Katok
Edited by
Boris Hasselblatt
In this book, which arose from an MSRI research workshop cosponspored
by the Clay Mathematical Institute, leading experts give an overview
of several areas of dynamical systems that have recently experienced
substantial progress.
In symplectic geometry, a fast-growing field having its roots in
classical mechanics, Cieliebak, Hofer, Latschev and Schlenk give a
definitive survey of quantitative techniques and symplectic
capacities, which have become a central research tool. Fisher's
survey on local rigidity of group actions is a broad and up-to-date
account of a flourishing subject built on the fact that for actions of
noncyclic groups, topological conjugacy commonly implies smooth
conjugacy.
Other articles by Eigen, Feres, Kochergin, Krieger, Navarro, Pinto,
Prasad, Rand and Robinson cover subjects in hyperbolic, parabolic and
symbolic dynamics as well as ergodic theory. Among the specific areas
of interest are random walks and billiards, diffeomorphisms and flows
on surfaces, amenability and tilings.
The articles are complemented by a fifty-page commented problem list,
compiled by the editor with the help of numerous specialists. Several
sections of this list focus on problems beyond the areas covered in
the surveys, and all are sure to inspire and guide further research.