Ergodic Optimization in the Expanding Case
Concepts, Tools and Applications
Lieferzeit: Print on Demand - Lieferbar innerhalb von 3-5 Werktagen I
ISBN-13:
9783319666426
Veröffentl:
2017
Seiten:
73
Autor:
Eduardo Garibaldi
Gewicht:
156 g
Format:
236x156x8 mm
Serie:
SpringerBriefs in Mathematics
Sprache:
Englisch
Beschreibung:
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.
Provides an innovative and useful approach to ergodic optimization for a broader audience
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.