Ergodic Optimization in the Expanding Case : Concepts, Tools and Applications. 1st ed. 2017

種類:

電子ブック

責任表示:

by Eduardo Garibaldi

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Garibaldi, Eduardo.
• SpringerLink (Online service)

シリーズ名:

SpringerBriefs in Mathematics ;

ISBN:

9783319666433 [3319666436]    

注記:

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.
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.

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