Ergodic Optimization in the Expanding Case : Concepts, Tools and Applications / by Eduardo Garibaldi.

Format:

Book

Author/Creator:

Garibaldi, Eduardo., Author.

Series:

SpringerBriefs in Mathematics, 2191-8198

Language:

English

Subjects (All):

Dynamics.

Ergodic theory.

Calculus of variations.

Mathematical optimization.

Thermodynamics.

Solid state physics.

Dynamical Systems and Ergodic Theory.

Calculus of Variations and Optimal Control; Optimization.

Continuous Optimization.

Solid State Physics.

Local Subjects:

Dynamical Systems and Ergodic Theory.

Calculus of Variations and Optimal Control; Optimization.

Continuous Optimization.

Thermodynamics.

Solid State Physics.

Physical Description:

1 online resource (VIII, 73 p.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

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.

Contents:

Chapter 01- Introduction

Chapter 02- Duality

Chapter 03- Calibrated sub-actions

Chapter 04- Aubry set.-Chapter 05- Mañé potential and Peierls barrier

Chapter 06- Representation of calibrated sub-actions

Chapter 07- Separating sub-actions

Chapter 08- Further properties of sub-actions

Chapter 09- Relations with the thermodynamic formalism

Appendix- Bounded measurable sub-actions

Bibliography.

Notes:

Includes bibliographical references and index.

ISBN:

3-319-66643-6