Ergodic optimization in the expanding case : concepts, tools and applications

Description

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. Front Matter ....Pages i-viii Introduction (Eduardo Garibaldi)....Pages 1-7 Duality (Eduardo Garibaldi)....Pages 9-12 Calibrated Sub-actions (Eduardo Garibaldi)....Pages 13-20 Aubry Set (Eduardo Garibaldi)....Pages 21-25 Mañé Potential and Peierls Barrier (Eduardo Garibaldi)....Pages 27-36 Representation of Calibrated Sub-actions (Eduardo Garibaldi)....Pages 37-40 Separating Sub-actions (Eduardo Garibaldi)....Pages 41-45 Further Properties of Sub-actions (Eduardo Garibaldi)....Pages 47-51 Relations with the Thermodynamic Formalism (Eduardo Garibaldi)....Pages 53-63 Back Matter ....Pages 65-73