Ergodic Optimization in the Expanding Case
Concepts, Tools and Applications
Published on 21. September 2017
VIII, 73 pages
978-3-319-66643-3 (ISBN)
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.
More details
Series
Edition
1st ed. 2017
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Primary & secondary/elementary & high school
Product notice
Reflowable
Illustrations
VIII, 73 p.
File size
1,13 MB
ISBN-13
978-3-319-66643-3 (9783319666433)
DOI
10.1007/978-3-319-66643-3
Schweitzer Classification
Other editions
Additional editions
Book
09/2017
Springer
€53.49
Shipment within 10-15 days
Person
Eduardo Garibaldi holds a PhD in Mathematics from the Federal University of Rio Grande do Sul, Brazil, and an MA from the IMPA - National Institute for Pure and Applied Mathematics, Brazil, having pursued postdoctoral studies at the Université Bordeaux, France. He is currently affiliated with the University of Campinas, Brazil, and his research efforts chiefly focus on dynamical systems and ergodic theory, motivated by problems from equilibrium statistical mechanics and solid state physics.
Content
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.
