Thermodynamic Formalism And Holomorphic Dynamical Systems
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Thermodynamic Formalism And Holomorphic Dynamical Systems
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Author : Michel Zinsmeister
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Thermodynamic Formalism And Holomorphic Dynamical Systems written by Michel Zinsmeister and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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.
Thermodynamic Formalism
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Author : David Ruelle
language : en
Publisher: Cambridge University Press
Release Date : 2004-11-25
Thermodynamic Formalism written by David Ruelle and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-25 with Science categories.
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.
Thermodynamic Formalism
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Author : David Ruelle
language : en
Publisher:
Release Date : 2004
Thermodynamic Formalism written by David Ruelle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Electronic books categories.
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.
Thermodynamic Formalism And Applications To Dimension Theory
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Author :
language : en
Publisher: Springer
Release Date : 2011-08-24
Thermodynamic Formalism And Applications To Dimension Theory written by and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-24 with categories.
Finer Thermodynamic Formalism Distance Expanding Maps And Countable State Subshifts Of Finite Type Conformal Gdmss Lasota Yorke Maps And Fractal Geometry
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Author : Mariusz Urbański
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-05-23
Finer Thermodynamic Formalism Distance Expanding Maps And Countable State Subshifts Of Finite Type Conformal Gdmss Lasota Yorke Maps And Fractal Geometry written by Mariusz Urbański and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-23 with Mathematics categories.
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.
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
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Author : Mariusz Urbański
language : en
Publisher:
Release Date : 2022
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 written by Mariusz Urbański and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Dynamics categories.
"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
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Author : Mariusz Urbański
language : en
Publisher: de Gruyter
Release Date : 2022
Ergodic Theory Finite And Infinite Thermodynamic Formalism Symbolic Dynamics And Distance Expanding Maps written by Mariusz Urbański and has been published by de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Mathematics categories.
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.
Non Invertible Dynamical Systems Ergodic Theory Finite And Infinite Thermodynamic Formalism Symbolic Dynamics And Distance Expanding Maps
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Author : Mariusz Urbański
language : en
Publisher:
Release Date : 2022
Non Invertible Dynamical Systems Ergodic Theory Finite And Infinite Thermodynamic Formalism Symbolic Dynamics And Distance Expanding Maps written by Mariusz Urbański and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Dynamics categories.
"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
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Author : Mariusz Urbański
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-11-22
Ergodic Theory Finite And Infinite Thermodynamic Formalism Symbolic Dynamics And Distance Expanding Maps written by Mariusz Urbański and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-22 with Mathematics categories.
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.
Dynamical Systems And Statistical Mechanics
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Author : I͡Akov Grigorʹevich Sinaĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Dynamical Systems And Statistical Mechanics written by I͡Akov Grigorʹevich Sinaĭ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Dynamical systems and statistical mechanics have been developing in close interaction during the past decade, and the papers in this book attest to the productiveness of this interaction. The first paper in the collection contains a new result in the theory of quantum chaos, a burgeoning line of inquiry which combines mathematics and physics and which is likely in time to produce many new connections and applications. Another paper, related to the renormalization group method for the study of maps of the circle with singularities due to a jump in the derivative, demonstrates that the fixed point of the renormgroup can in this case be sufficiently described. In certain situations, the renormgroup methods work better than the traditional KAM method. Other topics covered include: thermodynamic formalism for certain infinite-dimensional dynamical systems, numerical simulation of dynamical systems with hyperbolic behaviour, periodic points of holomorphic maps, the theory of random media, statistical properties of the leading eigenvalue in matrix ensembles of large dimension, spectral properties of the one-dimensional Schrodinger operator. This volume will appeal to many readers, as it covers a broad range of topics and presents a view of some of the frontier research in the Soviet Union today.