Titlebook: Ergodic Optimization in the Expanding Case; Concepts, Tools and Eduardo Garibaldi Book 2017 The Author(s) 2017 ergodic optimization.weak K

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Riyaz Ahmad Mir,Khurshid Ahmad Lonest possible subset of the phase space, that is, on the Aubry set. Named separating sub-actions, we will show how they can be obtained from non-trivial convex combinations of the members of the family of calibrated sub-actions given by the Peierls barrier or by the Mañé potential.

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Further Properties of Sub-actions,ials that are not cohomologous to a constant, the separating sub-actions explicitly constructed in the previous chapter are quite particular and actually represent a small part of the whole set of Lipschitz continuous separating sub-actions.

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Book 2017k 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..

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2191-8198 evance 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..978-3-319-66642-6978-3-319-66643-3Series ISSN 2191-8198 Series E-ISSN 2191-8201