Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous.
While a good understanding of the onset of chaos has been achieved, using as a …

4. Topological Markov chains 297 12. The zeta function of an A#-homeomorphism 316 S.
Locally maximal hyperbolic sets 302 13. The maximal entropy measure and the distribution …

In order to describe the problems and results, treated in this paper, in more detail, I shall first
review the ideas of [19], also comparing them with those ecposed by Landau and Lifschitz …

Symbolic dynamics is a mature yet rapidly developing area of dynamical systems. It has
established strong connections with many areas, including linear algebra, graph theory …

This book is an updated version of the information theory classic, first published in 1990.
About one-third of the book is devoted to Shannon source and channel coding theorems; the …

Reissued in the Cambridge Mathematical Library this classic book outlines the theory of
thermodynamic formalism which was developed to describe the properties of certain …

Many phenomena in physics, chemistry, and biology can be modelled by spatial random
processes. One such process is continuum percolation, which is used when the …

Ergodic theory in its broadest sense is the study of group actions on measure spaces.
Historically the discipline has tended to concentrate on the framework of integer actions, in …

In this paper we present a class of C*-algebras and point out its close relationship to
topological Markov chains, whose theory is part of symbolic dynamics. The C*-algebra …

This book introduces modern ergodic theory. It emphasizes a new approach that relies on
the technique of joining two (or more) dynamical systems. This approach has proved to be …