Ergodic Optimization in the Expanding Case (eBook)

Concepts, Tools and Applications

Eduardo Garibaldi (Autor)

eBook Download: PDF

2017 | 1st ed. 2017
73 Seiten
Springer International Publishing (Verlag)
978-3-319-66643-3 (ISBN)

Infos

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.

Autor

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.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 21.9.2017
• Reihe/Serie: SpringerBriefs in Mathematics
• Reihe/Serie: SpringerBriefs in Mathematics
• Zusatzinfo: VIII, 73 p.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Schlagworte: Aubry set • ergodic optimization • Mañé potential • sub-actions • thermodynamics • weak KAM
• ISBN-10: 3-319-66643-6 / 3319666436
• ISBN-13: 978-3-319-66643-3 / 9783319666433