Ergodic Optimization in the Expanding Case Concepts, Tools and Applications /

• Main Author: Garibaldi, Eduardo (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: SpringerBriefs in Mathematics,
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Calculus of variations.; Mathematical optimization.; Thermodynamics.; Solid state physics.; Dynamical Systems and Ergodic Theory.; Calculus of Variations and Optimal Control; Optimization.; Continuous Optimization.; Solid State Physics.
• Physical Description: VIII, 73 p. online resource.
• ISBN: 9783319666433
• ISSN: 2191-8198

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.