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Ergodic Optimization in the Expanding Case

Concepts, Tools and Applications

  • Book
  • © 2017

Overview

Authors:
  1. Eduardo Garibaldi

    1. University of Campinas - IMECC, Campinas, Brazil

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  • Provides an innovative and useful approach to ergodic optimization for a broader audience
  • Explores the power of Sub-actions as tools for Symbolic Dynamics
  • Describes the relations between ergodic optimization theory and thermodynamic formalism
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Eduardo Garibaldi
    Pages 1-7

  3. Duality

    • Eduardo Garibaldi
    Pages 9-12

  4. Calibrated Sub-actions

    • Eduardo Garibaldi
    Pages 13-20

  5. Aubry Set

    • Eduardo Garibaldi
    Pages 21-25

  6. Mañé Potential and Peierls Barrier

    • Eduardo Garibaldi
    Pages 27-36

  7. Representation of Calibrated Sub-actions

    • Eduardo Garibaldi
    Pages 37-40

  8. Separating Sub-actions

    • Eduardo Garibaldi
    Pages 41-45

  9. Further Properties of Sub-actions

    • Eduardo Garibaldi
    Pages 47-51

  10. Relations with the Thermodynamic Formalism

    • Eduardo Garibaldi
    Pages 53-63

  11. Back Matter

    Pages 65-73
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Keywords

About this book

This book focuses on the interpretation of ergodic optimal problems as questions of variational dynamics, employing a comparable approach to that of the Aubry-Mather theory for Lagrangian systems. Ergodic optimization is primarily concerned with the study of optimizing probability measures. This work presents and discusses the fundamental concepts of the theory, including the use and relevance of Sub-actions as analogues to subsolutions of the Hamilton-Jacobi equation. Further, it provides evidence for the impressively broad applicability of the tools inspired by the weak KAM theory.



Authors and Affiliations

  • University of Campinas - IMECC, Campinas, Brazil

    Eduardo Garibaldi

About the author

Eduardo Garibaldi holds a PhD in Mathematics from the Federal University of Rio Grande do Sul, Brazil, and an MA from the IMPA – National Institute for Pure and Applied Mathematics, Brazil, having pursued postdoctoral studies at the Université Bordeaux, France. He is currently affiliated with the University of Campinas, Brazil, and his research efforts chiefly focus on dynamical systems and ergodic theory, motivated by problems from equilibrium statistical mechanics and solid state physics.



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