Author : Thomas Kempton
Publisher :
Page : 0 pages
File Size : 39,28 MB
Release : 2011
Category :
ISBN :
Thermodynamic Formalism for Symbolic Dynamical Systems
Thomas Kempton
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Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps
Mariusz Urbański
Author : Mariusz Urbański
Publisher : Walter de Gruyter GmbH & Co KG
Page : 458 pages
File Size : 10,67 MB
Release : 2021-11-22
Category : Mathematics
ISBN : 3110702681
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.
Thermodynamic Formalism and Applications to Dimension Theory
Luis Barreira
Author : Luis Barreira
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 10,4 MB
Release : 2011-08-24
Category : Mathematics
ISBN : 3034802064
This self-contained monograph presents a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to dimension theory and multifractal analysis of dynamical systems. In particular, the book considers three different flavors of the thermodynamic formalism, namely nonadditive, subadditive, and almost additive, and provides a detailed discussion of some of the most significant results in the area, some of them quite recent. It also includes a discussion of the most substantial applications of these flavors of the thermodynamic formalism to dimension theory and multifractal analysis of dynamical systems.
Non-invertible Dynamical Systems: Ergodic theory : finite and infinite, thermodynamic formalism, symbolic dynamics and distance expanding maps
Mariusz Urbański
Author : Mariusz Urbański
Publisher :
Page : 0 pages
File Size : 25,53 MB
Release : 2022
Category : Dynamics
ISBN :
"This book consists of three volumes. The first volume contains introductory accounts of topological dynamical systems, fi nite-state symbolic dynamics, distance expanding maps, and ergodic theory of metric dynamical systems acting on probability measure spaces, including metric entropy theory of Kolmogorov and Sinai. More advanced topics comprise infi nite ergodic theory, general thermodynamic formalism, topological entropy and pressure. Thermodynamic formalism of distance expanding maps and countable-alphabet subshifts of fi nite type, graph directed Markov systems, conformal expanding repellers, and Lasota-Yorke maps are treated in the second volume, which also contains a chapter on fractal geometry and its applications to conformal systems. Multifractal analysis and real analyticity of pressure are also covered. The third volume is devoted to the study of dynamics, ergodic theory, thermodynamic formalism and fractal geometry of rational functions of the Riemann sphere." --Provided by publisher.
Ergodic Theory - Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps
Mariusz Urbański
Author : Mariusz Urbański
Publisher : de Gruyter
Page : 0 pages
File Size : 22,65 MB
Release : 2022
Category : Mathematics
ISBN : 9783110702644
The book contains detailed treatment of thermodynamic formalism. Topological pressure, entropy, variational principle, and equilibrium states are presented in detail in the first volume. Abstract ergodic theory is also given a significant attention.
Thermodynamic Formalism and Holomorphic Dynamical Systems
Michel Zinsmeister
Author : Michel Zinsmeister
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 18,53 MB
Release : 2000
Category : Mathematics
ISBN : 9780821819487
The purpose of thermodynamics and statistical physics is to understand the equilibrium of a gas or the different states of matter. To understand the strange fractal sets appearing when one iterates a quadratic polynomial is one of the goals of the theory of holomorphic dynamical systems. These two theories are strongly linked: The laws of thermodynamics happen to be an extremely powerful tool for understanding the objects of holomorphic dynamical systems. A "thermodynamic formalism" has been developed, bringing together notions that are a priori unrelated. While the deep reasons of this parallelism remain unknown, the goal of this book is to describe this formalism both from the physical and mathematical point of view in order to understand how it works and how useful it can be. This translation is a slightly revised version of the original French edition. The main changes are in Chapters 5 and 6 and consist of clarification of some proofs and a new presentation of the basics in iteration of polynomials.
Finer Thermodynamic Formalism – Distance Expanding Maps and Countable State Subshifts of Finite Type, Conformal GDMSs, Lasota-Yorke Maps and Fractal Geometry
Mariusz Urbański
Author : Mariusz Urbański
Publisher : Walter de Gruyter GmbH & Co KG
Page : 524 pages
File Size : 27,98 MB
Release : 2022-05-23
Category : Mathematics
ISBN : 311070269X
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.
Thermodynamic Formalism
Mark Pollicott
Author : Mark Pollicott
Publisher : Springer Nature
Page : 536 pages
File Size : 16,56 MB
Release : 2021-10-01
Category : Mathematics
ISBN : 3030748634
This volume arose from a semester at CIRM-Luminy on “Thermodynamic Formalism: Applications to Probability, Geometry and Fractals” which brought together leading experts in the area to discuss topical problems and recent progress. It includes a number of surveys intended to make the field more accessible to younger mathematicians and scientists wishing to learn more about the area. Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry. This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.
Non-invertible Dynamical Systems: Finer thermodynamic formalism : distance expanding maps and countable state subshifts of finite type, conformal GDMSs, Lasota-Yorke maps and fractal geometry
Mariusz Urbański
Author : Mariusz Urbański
Publisher :
Page : 0 pages
File Size : 16,24 MB
Release : 2022
Category : Dynamics
ISBN :
"This book consists of three volumes. The first volume contains introductory accounts of topological dynamical systems, fi nite-state symbolic dynamics, distance expanding maps, and ergodic theory of metric dynamical systems acting on probability measure spaces, including metric entropy theory of Kolmogorov and Sinai. More advanced topics comprise infi nite ergodic theory, general thermodynamic formalism, topological entropy and pressure. Thermodynamic formalism of distance expanding maps and countable-alphabet subshifts of fi nite type, graph directed Markov systems, conformal expanding repellers, and Lasota-Yorke maps are treated in the second volume, which also contains a chapter on fractal geometry and its applications to conformal systems. Multifractal analysis and real analyticity of pressure are also covered. The third volume is devoted to the study of dynamics, ergodic theory, thermodynamic formalism and fractal geometry of rational functions of the Riemann sphere." --Provided by publisher.
Thermodynamic Formalism
David Ruelle
Author : David Ruelle
Publisher : Cambridge University Press
Page : 198 pages
File Size : 30,19 MB
Release : 2004-11-25
Category : Science
ISBN : 9781139455282
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.