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Author: Gerhard Keller
Publisher: Cambridge University Press
Published: 1998-01-22
Total Pages: 196
ISBN-13: 9780521595346
DOWNLOAD EBOOK →Based on a one semester course, this book provides a self contained introduction to the ergodic theory of equilibrium states.
Author: Robert Edward Bowen
Publisher: Springer Science & Business Media
Published: 2008-04-18
Total Pages: 84
ISBN-13: 3540776052
DOWNLOAD EBOOK →For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details. From the Preface by D. Ruelle: "Rufus Bowen has left us a masterpiece of mathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have been proved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems."
Author: Robert Edward Bowen
Publisher: Springer
Published: 2009-08-29
Total Pages: 80
ISBN-13: 9783540848875
DOWNLOAD EBOOK →For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details. From the Preface by D. Ruelle: "Rufus Bowen has left us a masterpiece of mathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have been proved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems."
Author: R. Bowen
Publisher:
Published: 2014-01-15
Total Pages: 120
ISBN-13: 9783662192702
DOWNLOAD EBOOK →Author: Mariusz Urbański
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2021-11-22
Total Pages: 458
ISBN-13: 3110702681
DOWNLOAD EBOOK →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.
Author: Cesar E. Silva
Publisher: Springer Nature
Published: 2023-07-31
Total Pages: 707
ISBN-13: 1071623885
DOWNLOAD EBOOK →This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras
Author: Zhiqiang Li
Publisher: Springer
Published: 2017-04-06
Total Pages: 182
ISBN-13: 9462391742
DOWNLOAD EBOOK →Thurston maps are topological generalizations of postcritically-finite rational maps. This book provides a comprehensive study of ergodic theory of expanding Thurston maps, focusing on the measure of maximal entropy, as well as a more general class of invariant measures, called equilibrium states, and certain weak expansion properties of such maps. In particular, we present equidistribution results for iterated preimages and periodic points with respect to the unique measure of maximal entropy by investigating the number and locations of fixed points. We then use the thermodynamical formalism to establish the existence, uniqueness, and various other properties of the equilibrium state for a Holder continuous potential on the sphere equipped with a visual metric. After studying some weak expansion properties of such maps, we obtain certain large deviation principles for iterated preimages and periodic points under an additional assumption on the critical orbits of the maps. This enables us to obtain general equidistribution results for such points with respect to the equilibrium states under the same assumption.
Author: Neil Dobbs
Publisher: American Mathematical Society
Published: 2023-06-22
Total Pages: 116
ISBN-13: 1470461269
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Author: David Ruelle
Publisher: Cambridge University Press
Published: 2004-11-25
Total Pages: 198
ISBN-13: 9781139455282
DOWNLOAD EBOOK →Reissued in the Cambridge Mathematical Library this classic book outlines the theory of thermodynamic formalism which was developed to describe the properties of certain physical systems consisting of a large number of subunits. It is aimed at mathematicians interested in ergodic theory, topological dynamics, constructive quantum field theory, the study of certain differentiable dynamical systems, notably Anosov diffeomorphisms and flows. It is also of interest to theoretical physicists concerned with the conceptual basis of equilibrium statistical mechanics. The level of the presentation is generally advanced, the objective being to provide an efficient research tool and a text for use in graduate teaching. Background material on mathematics has been collected in appendices to help the reader. Extra material is given in the form of updates of problems that were open at the original time of writing and as a new preface specially written for this new edition by the author.
Author: Marcelo Viana
Publisher: Cambridge University Press
Published: 2016-02-15
Total Pages: 547
ISBN-13: 1107126967
DOWNLOAD EBOOK →Self-contained introductory textbook suitable for a variety of one- or two-semester courses. Rich with examples, applications and exercises.
