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Thermodynamic Formalism

CIRM Jean-Morlet Chair, Fall 2019

  • Conference proceedings
  • © 2021

Overview

Editors:
  1. Mark Pollicott

    1. Department of Mathematics, Warwick University, Coventry, UK

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  2. Sandro Vaienti

    1. Institute de Mathématiques de Toulon, Toulon, France;, Centre de Physique Théorique de Luminy, Marseille, France

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    You can also search for this editor in PubMed   Google Scholar

  • The first book in the area of thermodynamic formalism, there are no obvious comparable books
  • Provides insight into the current state of research
  • Accessible to a broad range of lecturers

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2290)

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Table of contents (16 papers)

  1. Front Matter

    Pages i-xiv
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  2. Specification and Expansiveness

    1. Front Matter

      Pages 1-1
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    2. Beyond Bowen’s Specification Property

      • Vaughn Climenhaga, Daniel J. Thompson
      Pages 3-82

    3. The Role of Continuity and Expansiveness on Leo and Periodic Specification Properties

      • Serge Troubetzkoy, Paulo Varandas
      Pages 83-96

  3. Low Dimensional Dynamics and Thermodynamic Formalism

    1. Front Matter

      Pages 97-97
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    2. Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions

      • Volker Mayer, Mariusz Urbański
      Pages 99-139

  4. Probability Theory, Ergodicity and Thermodynamic Formalism

    1. Front Matter

      Pages 141-141
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    2. Recurrent Sets for Ergodic Sums of an Integer Valued Function

      • Jean-Pierre Conze
      Pages 143-175

    3. Almost Sure Invariance Principle for Random Distance Expanding Maps with a Nonuniform Decay of Correlations

      • Davor Dragičević, Yeor Hafouta
      Pages 177-204

    4. Limit Theorem for Reflected Random Walks

      • Hoang-Long Ngo, Marc Peigné
      Pages 205-233

    5. The Strong Borel–Cantelli Property in Conventional and Nonconventional Setups

      • Yuri Kifer
      Pages 235-261

    6. Application of the Convergence of the Spatio-Temporal Processes for Visits to Small Sets

      • Françoise Pène, Benoît Saussol
      Pages 263-288

  5. Geometry and Thermodynamic Formalism

    1. Front Matter

      Pages 289-289
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    2. Rate of Mixing for Equilibrium States in Negative Curvature and Trees

      • Anne Broise-Alamichel, Jouni Parkkonen, Frédéric Paulin
      Pages 291-315

    3. Statistical Properties of the Rauzy-Veech-Zorich Map

      • Romain Aimino, Mark Pollicott
      Pages 317-349

    4. Entropy Rigidity, Pressure Metric, and Immersed Surfaces in Hyperbolic 3-Manifolds

      • Lien-Yung Kao
      Pages 351-393

    5. Higher Teichmüller Theory for Surface Groups and Shifts of Finite Type

      • Mark Pollicott, Richard Sharp
      Pages 395-418

  6. Fractal Geometry

    1. Front Matter

      Pages 419-419
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    2. Dimension Estimates for C 1 Iterated Function Systems and C 1 Repellers, a Survey

      • De-Jun Feng, Károly Simon
      Pages 421-467

    3. Intermediate Dimensions: A Survey

      • Kenneth J. Falconer
      Pages 469-493
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, Warwick University, Coventry, UK

    Mark Pollicott

  • Institute de Mathématiques de Toulon, Toulon, France;, Centre de Physique Théorique de Luminy, Marseille, France

    Sandro Vaienti

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