Thermodynamic formalism for countable symbolic Markov chains

Abstract

Contents Introduction Chapter I. Variational principles and a classification of functions defined on a Markov set §1. Main definitions. The variational principle for topological pressure §2. Generating functions. Non-negative matrices §3. Criteria for stable positiveness §4. Equilibrium and Gibbs measures. Gibbs' variational principle Chapter II. Two classes of invariant measures related to symbolic Markov chains. The method of subdifferentials §5. The subdifferential of topological pressure §6. Asymptotically equilibrium measures. Convergence of equilibrium measures corresponding to finite subchains of a countable symbolic Markov chain §7. Asymptotics of discrete invariant measures Chapter III. Dynamic zeta functions related to symbolic Markov chains §8. The factorization theorem and some corollaries §9. Meromorphic continuation of zeta functions and the behaviour of discrete invariant measures §10. The zeta function and spectral properties of non-negativematrices Chapter IV. Some special classes of symbolic Markov chains §11. Symbolic Markov chains with a regular set of periodic orbits §12. Symbolic Markov chains with finite cycle-passage domainBibliography