Ergodic Optimization in the Expanding Case

Concepts, Tools and Applications

Eduardo Garibaldi (Autor)

Buch | Softcover

VIII, 73 Seiten

2017 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-66642-6 (ISBN)

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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.

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.

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.

Erscheinungsdatum	11.10.2017
Reihe/Serie	SpringerBriefs in Mathematics
Zusatzinfo	VIII, 73 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	142 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Aubry set • Calculus of Variations • Calculus of Variations and Optimal Control • Continuous Optimization • Dynamical Systems and Ergodic Theory • ergodic optimization • Mañé potential • Mathematics • mathematics and statistics • Nonlinear Science • Optimization • Solid state physics • Spectrum analysis, spectrochemistry, mass spectrom • sub-actions • thermodynamics • Thermodynamics & heat • Thermodynamics & heat • weak KAM
ISBN-10	3-319-66642-8 / 3319666428
ISBN-13	978-3-319-66642-6 / 9783319666426
Zustand	Neuware