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

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.

List of contents

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.

About the author

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.

Summary

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.

Product details

• Authors: Eduardo Garibaldi
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2017
• EAN: 9783319666426
• ISBN: 978-3-31-966642-6
• No. of pages: 73
• Dimensions: 156 mm x 8 mm x 236 mm
• Weight: 156 g
• Illustrations: VIII, 73 p.
• Series: SpringerBriefs in Mathematics; SpringerBriefs in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; C, Optimization, Dynamics, Mathematics and Statistics, Solid State Physics, Thermodynamics, Thermodynamics & heat, Electronic Devices, Spectrum analysis, spectrochemistry, mass spectrometry, Dynamical Systems and Ergodic Theory, Ergodic theory, Dynamical systems, Mathematical optimization, Calculus of Variations and Optimization, Calculus of variations, Calculus of Variations and Optimal Control; Optimization, Continuous Optimization