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 wor...

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Main Author: Garibaldi, Eduardo. (Author, http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
Edition:1st ed. 2017.
Series:SpringerBriefs in Mathematics,
Subjects:
Online Access:https://doi.org/10.1007/978-3-319-66643-3
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245 1 0 |a Ergodic Optimization in the Expanding Case  |h [electronic resource] :  |b Concepts, Tools and Applications /  |c by Eduardo Garibaldi. 
250 |a 1st ed. 2017. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Springer,  |c 2017. 
300 |a VIII, 73 p.  |b online resource. 
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505 0 |a 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. 
520 |a 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. 
650 0 |a Dynamics. 
650 0 |a Ergodic theory. 
650 0 |a Calculus of variations. 
650 0 |a Mathematical optimization. 
650 0 |a Thermodynamics. 
650 0 |a Solid state physics. 
650 1 4 |a Dynamical Systems and Ergodic Theory.  |0 https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 
650 2 4 |a Calculus of Variations and Optimal Control; Optimization.  |0 https://scigraph.springernature.com/ontologies/product-market-codes/M26016 
650 2 4 |a Continuous Optimization.  |0 https://scigraph.springernature.com/ontologies/product-market-codes/M26030 
650 2 4 |a Thermodynamics.  |0 https://scigraph.springernature.com/ontologies/product-market-codes/P21050 
650 2 4 |a Solid State Physics.  |0 https://scigraph.springernature.com/ontologies/product-market-codes/P25013 
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