Ergodic Optimization in the Expanding Case

Concepts, Tools and Applications
1. Auflage 2017
ISBN: 978-3-319-66642-6
Verlag: Springer

Buch, Englisch, 73 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1416 g

Reihe: SpringerBriefs in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Garibaldi, Eduardo

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung

Inhaltsverzeichnis

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.

Über Autor(innen)

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.