Ergodic optimization in the expanding case : concepts, tools and applications / Eduardo Garibaldi.
Garibaldi, Eduardo.
2017
QA402.5
Available Online

Linked e-resources

Linked Resource Online Access
Concurrent users Unlimited
Authorized users Authorized users
Document Delivery Supplied Can lend chapters, not whole ebooks

Details

Title Ergodic optimization in the expanding case : concepts, tools and applications / Eduardo Garibaldi.
Author Garibaldi, Eduardo.
ISBN 9783319666433 (electronic book)
3319666436 (electronic book)
9783319666426
3319666428
Publication Details Cham : Springer, 2017.
Language English
Description 1 online resource.
Call Number QA402.5
Dewey Decimal Classification 519.6
510
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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Series SpringerBriefs in mathematics.
Available in Other Form Print version: 3319666428
Linked Resources Online Access
Record Appears in Online Resources > Ebooks
All Resources
Preface; Contents; 1 Introduction; 1.1 Theoretical Interactions; 1.2 Basic Notions; 1.3 Organization of the Text; 2 Duality; 2.1 A Multifaceted Constant; 2.2 The Dual Formula; 3 Calibrated Sub-actions; 3.1 An Iterative Approximation Approach; 3.2 Asymptotic Behavior of Lax-Oleinik Operators; 4 Aubry Set; 4.1 A Maximizing Non-wandering Set; 5 Mañé Potential and Peierls Barrier; 5.1 Action Functionals in Ergodic Optimization; 5.2 Mañé Potential and Kleene Star; 6 Representation of Calibrated Sub-actions; 6.1 The Mañé-Peierls Transform; 7 Separating Sub-actions; 7.1 A Minimalist Sub-action

8 Further Properties of Sub-actions8.1 Convexity, Non-compactness, and Extremal Elements; 9 Relations with the Thermodynamic Formalism; 9.1 Equilibrium States and Maximizing Measures; 9.2 Examples of Convergence of Equilibrium States; Appendix A Bounded Measurable Sub-actions; Maximizing Sets; Bibliography; Index

Browse Subjects

Show more subjects...

Statistics

from
to
Export