Download or read book Ergodic theory of equilibrium states for rational maps written by Manfred Denker and published by . This book was released on 1989 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ergodic Theory of Expanding Thurston Maps written by Zhiqiang Li and published by Springer. This book was released on 2017-04-06 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Equilibrium States in Ergodic Theory written by Gerhard Keller and published by Cambridge University Press. This book was released on 1998-01-22 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a one semester course, this book provides a self contained introduction to the ergodic theory of equilibrium states.
Download or read book Ergodic Theory of Equilibrium States for Rational Maps written by M. Denker and published by . This book was released on 1989 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ergodic Theory Finite and Infinite Thermodynamic Formalism Symbolic Dynamics and Distance Expanding Maps written by Mariusz Urbański and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-11-22 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Ergodic Theory and Related Topics III written by Ulrich Krengel and published by Springer. This book was released on 2006-11-14 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the conference was to represent recent developments in measure theoretic, differentiable and topological dynamical systems as well as connections to probability theory, stochastic processes, operator theory and statistical physics. Only original research papers that do not appear elsewhere are included in the proceedings. Their topics include: C(2)-diffeomorphisms of compact Riemann manifolds, geodesic flows, chaotic behaviour in billards, nonlinear ergodic theory, central limit theorems for subadditive processes, Hausdorff measures for parabolic rational maps, Markov operators, periods of cycles, Julia sets, ergodic theorems. From the Contents: L.A. Bunimovich: On absolutely focusing mirrors.- M. Denker, M. Urbanski: The dichotomy of Hausdorff measures and equilibrium states for parabolic rational maps.- F. Ledrappier: Ergodic properties of the stable foliations.- U. Wacker: Invariance principles and central limit theorems for nonadditive stationary processes.- J. Schmeling, R. Siegmund-Schultze: Hoelder continuity of the holonomy map for hyperbolic basic sets.- A.M. Blokh: The spectral decomposition, periods of cycles and Misiurewicz conjecture for graph maps.- and contributions by Chr. Bandt and K. Keller, T. Bogenschutz andH. Crauel, H.G. Bothe, M. Denker and K.F. Kramer, T.P. Hill and U. Krengel, A. Iwanik, Z.S. Kowalski, E. Lesigne, J. Malczak, I. Mizera, J. Sipos, R. Wittmann.
Download or read book Ergodic Theory Finite and Infinite Thermodynamic Formalism Symbolic Dynamics and Distance Expanding Maps written by Mariusz Urbański and published by de Gruyter. This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms written by R. Bowen and published by . This book was released on 2014-01-15 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Equilibrium States and the Ergodic Theory of Ansor Diffeomorphisms written by Rufus Bowen and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Equilibrium states and the ergodic theory of Anosov diffeomorphisms written by Rufus Bowen and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Free Energy and Equilibrium States for Families of Interval Maps written by Neil Dobbs and published by American Mathematical Society. This book was released on 2023-06-22 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Ergodic theory for Markov fibred systems and parabolic rational maps written by Jon Aaronson and published by . This book was released on 1990 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ergodic Theory for Markov Fibred Systems and Parabolic Rational Maps written by J. Aaronson and published by . This book was released on 1990 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ergodic Theory and Related Topics III written by Ulrich Krengel and published by Springer. This book was released on 1992-05-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the conference was to represent recent developments in measure theoretic, differentiable and topological dynamical systems as well as connections to probability theory, stochastic processes, operator theory and statistical physics. Only original research papers that do not appear elsewhere are included in the proceedings. Their topics include: C(2)-diffeomorphisms of compact Riemann manifolds, geodesic flows, chaotic behaviour in billards, nonlinear ergodic theory, central limit theorems for subadditive processes, Hausdorff measures for parabolic rational maps, Markov operators, periods of cycles, Julia sets, ergodic theorems. From the Contents: L.A. Bunimovich: On absolutely focusing mirrors.- M. Denker, M. Urbanski: The dichotomy of Hausdorff measures and equilibrium states for parabolic rational maps.- F. Ledrappier: Ergodic properties of the stable foliations.- U. Wacker: Invariance principles and central limit theorems for nonadditive stationary processes.- J. Schmeling, R. Siegmund-Schultze: Hoelder continuity of the holonomy map for hyperbolic basic sets.- A.M. Blokh: The spectral decomposition, periods of cycles and Misiurewicz conjecture for graph maps.- and contributions by Chr. Bandt and K. Keller, T. Bogenschutz andH. Crauel, H.G. Bothe, M. Denker and K.F. Kramer, T.P. Hill and U. Krengel, A. Iwanik, Z.S. Kowalski, E. Lesigne, J. Malczak, I. Mizera, J. Sipos, R. Wittmann.
Download or read book 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 published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-05-23 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book FREE ENERGY AND EQUILIBRIUM STATES FOR FAMILIES OF INTERVAL MAPS written by NEIL DOBBS; MIKE TODD. and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry and Topology in Dynamics written by Marcy Barge and published by American Mathematical Soc.. This book was released on 1999 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of the written presentations of lectures given at two special sessions: the AMS Special Session on Topology in Dynamics (Winston-Salem, NC) and the AMS-AWM Special Session on Geometry in Dynamics (San Antonio, TX). Each article concerns aspects of the topology or geometry of dynamical systems. Topics covered include the following: foliations and laminations, iterated function systems, the three-body problem, isotopy stability, homoclinic tangles, fractal dimension, Morse homology, knotted orbits, inverse limits, contact structures, Grassmanians, blowups, and continua. New results are presented reflecting current trends in topological aspects of dynamical systems. The book offers a wide variety of topics of special interest to those working this area bridging topology and dynamical systems.
