Weak Kam Methods And Ergodic Optimal Problems For Countable Markov Shifts

Weak KAM Methods and Ergodic Optimal Problems for Countable Markov Shifts

Issues in General and Specialized Mathematics Research: 2011 Edition

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Ergodic Optimization in the Expanding Case

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.