Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps

1. Auflage 2021
ISBN: 978-3-11-070264-4
Verlag: De Gruyter

Buch, Englisch, Band 69/1, 430 Seiten, Format (B × H): 170 mm x 240 mm, Gewicht: 900 g

Reihe: De Gruyter Expositions in Mathematics

The book contains a detailed treatment of thermodynamic formalism on general compact metrizable spaces. Topological pressure, topological entropy, variational principle, and equilibrium states are presented in detail. Abstract ergodic theory is also given a significant attention. Ergodic theorems, ergodicity, and Kolmogorov-Sinai metric entropy are fully explored. Furthermore, the book gives the reader an opportunity to find rigorous presentation of thermodynamic formalism for distance expanding maps and, in particular, subshifts of finite type over a finite alphabet. It also provides a fairly complete treatment of subshifts of finite type over a countable alphabet. Transfer operators, Gibbs states and equilibrium states are, in this context, introduced and dealt with. Their relations are explored. All of this is applied to fractal geometry centered around various versions of Bowen’s formula in the context of expanding conformal repellors, limit sets of conformal iterated function systems and conformal graph directed Markov systems. A unique introduction to iteration of rational functions is given with emphasize on various phenomena caused by rationally indifferent periodic points. Also, a fairly full account of the classicaltheory of Shub’s expanding endomorphisms is given; it does not have a book presentation in English language mathematical literature.

Zielgruppe

Researchers, graduate and postgraduate students on dynamical syst

Autoren/Hrsg.

Urbanski, Mariusz

Roy, Mario

Munday, Sara

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Stochastik
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Über Autor(innen)

Mariusz Urbanski, University of North Texas, USA; Mario Roy, York University, Toronto, Canada; Sara Munday, University of Pisa, Italy.