Affiliation:
1. UNICAMP – Department of Mathematics, 13083-859 Campinas – SP, Brazil
Abstract
Given a topological dynamical systems [Formula: see text], consider a sequence of continuous potentials [Formula: see text] that is asymptotically approached by sub-additive families. In a generalized version of ergodic optimization theory, one is interested in describing the set [Formula: see text] of [Formula: see text]-invariant probabilities that attain the following maximum value [Formula: see text] For this purpose, we extend the notion of Aubry set, denoted by [Formula: see text]. Our central result provides sufficient conditions for the Aubry set to be a maximizing set, i.e. [Formula: see text] belongs to [Formula: see text] if, and only if, its support lies on [Formula: see text]. Furthermore, we apply this result to the study of the joint spectral radius in order to show the existence of periodic matrix configurations approaching this value.
Publisher
World Scientific Pub Co Pte Lt
Cited by
3 articles.
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