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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Representation of Calibrated Sub-actions,can be used to describe all solutions of the Lax-Oleinik fixed point problem, that is, all calibrated sub-actions. The side effects of the analysis leading to such a result are the beginning of a deeper understanding of the nature of the sub-actions themselves.

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Separating Sub-actions,st 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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