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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果核

Biodegradation of Nitroaromatics by Microbes here covered, many of which have counterparts in Lagrangian Aubry-Mather theory. Our first step, nevertheless, consists in an attempt of placing ergodic optimization in the mathematical and physical research scenario.

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Improving Plants for Zinc Acquisition, In this chapter, some alternative expressions that could be considered to define the ergodic maximizing value are brought to the attention of the reader. Furthermore, a proof of the dual formula is provided.

CORE

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Biosorption of Ni(II) Using Seeds of 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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Endemic

Duality,ions. Since the earliest works in ergodic optimization theory, it became clear however that this constant can be presented in various equivalent ways. In this chapter, some alternative expressions that could be considered to define the ergodic maximizing value are brought to the attention of the rea

合唱团

Calibrated Sub-actions,ill show that calibrated sub-actions do exist and can be obtained as solutions of a Lax-Oleinik fixed point problem. Instead making use of a version of the classical Schauder-Tychonoff fixed point theorem, we apply a result due to Ishikawa regarding an iteration process for approximating fixed point

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Aubry Set,e first notion we present is the Aubry set, the part of the non-wandering set that characterizes the maximizing probabilities. Roughly speaking, the Aubry set is formed by the non-wandering points whose orbits have maximal Birkhoff sums. In the sequel, we give the precise definition and some example

内向者

,Mañé Potential and Peierls Barrier,onals will be available in ergodic optimization theory. The concepts that will be discussed in this chapter, namely, the Peierls barrier and the Mañé potential go back to the contributions of both Mather and Mañé in Lagrangian systems.