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Ergodic Optimization in the Expanding Case

Concepts, Tools and Applications

  • Eduardo Garibaldi

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Eduardo Garibaldi
    Pages 1-7
  3. Eduardo Garibaldi
    Pages 9-12
  4. Eduardo Garibaldi
    Pages 13-20
  5. Eduardo Garibaldi
    Pages 21-25
  6. Eduardo Garibaldi
    Pages 27-36
  7. Eduardo Garibaldi
    Pages 37-40
  8. Eduardo Garibaldi
    Pages 41-45
  9. Eduardo Garibaldi
    Pages 47-51
  10. Eduardo Garibaldi
    Pages 53-63
  11. Back Matter
    Pages 65-73

About this book

Introduction

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.

Keywords

ergodic optimization weak KAM sub-actions Aubry set Mañé potential thermodynamics

Authors and affiliations

  • Eduardo Garibaldi
    • 1
  1. 1.University of Campinas - IMECCCampinasBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-66643-3
  • Copyright Information The Author(s) 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-66642-6
  • Online ISBN 978-3-319-66643-3
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site