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＜E-Book＞
Ergodic Optimization in the Expanding Case : Concepts, Tools and Applications / by Eduardo Garibaldi
(SpringerBriefs in Mathematics. ISSN:21918201)

Edition	1st ed. 2017.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2017
Size	VIII, 73 p : online resource
Authors	*Garibaldi, Eduardo author SpringerLink (Online service)
Subjects	LCSH:Dynamical systems LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Thermodynamics LCSH:Condensed matter FREE:Dynamical Systems FREE:Calculus of Variations and Optimization FREE:Continuous Optimization FREE:Thermodynamics FREE:Condensed Matter Physics
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-319-66643-3

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