Ergodic Optimization in the Expanding Case

Concepts, Tools and Applications

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Calculus
Cover of the book Ergodic Optimization in the Expanding Case by Eduardo Garibaldi, Springer International Publishing
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Author: Eduardo Garibaldi ISBN: 9783319666433
Publisher: Springer International Publishing Publication: September 21, 2017
Imprint: Springer Language: English
Author: Eduardo Garibaldi
ISBN: 9783319666433
Publisher: Springer International Publishing
Publication: September 21, 2017
Imprint: Springer
Language: English

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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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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