This book covers one of the most exciting but most difficult topics in the modern theory of
dynamical systems: chaotic billiards. In physics, billiard models describe various mechanical …

In broad terms, the goal of dynamics is to describe the long-term evolution of systems for
which an" infinitesimal" evolution rule, such as a differential equation or the iteration of a …

In 438 alphabetically-arranged essays, this work provides a useful overview of the core
mathematical background for nonlinear science, as well as its applications to key problems …

We prove an almost sure invariance principle that is valid for general classes of
nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time …

We consider dynamical systems on domains that are not invariant under the dynamics—for
example, a system with a hole in the phase space—and raise issues regarding the meaning …

The connection between the thermodynamic description of transport phenomena and a
microscopic description of the underlying chaotic motion has recently received new attention …

While many dynamical systems of mechanical origin, in particular billiards, are strongly
chaotic—enjoy exponential mixing, the rates of mixing in many other models are slow …

We consider non-uniformly expanding maps on compact Riemannian manifolds of arbitrary
dimension, possibly having discontinuities and/or critical sets, and show that under some …

We prove large deviation principles for ergodic averages of dynamical systems admitting
Markov tower extensions with exponential return times. Our main technical result from which …

We investigate the statistical properties of a piecewise smooth dynamical system by directly
studying the action of the transfer operator on appropriate spaces of distributions. We …