Aubry set for asymptotically sub-additive potentials

Given a topological dynamical systems (Formula presented.), consider a sequence of continuous potentials (Formula presented.) that is asymptotically approached by sub-additive families. In a generalized version of ergodic optimization theory, one is interested in describing the set (Formula presented.) of (Formula presented.)-invariant probabilities that attain the following maximum value (Formula presented.) For this purpose, we extend the notion of Aubry set, denoted by (Formula presented.). Our central result provides sufficient conditions for the Aubry set to be a maximizing set, i.e. (Formula presented.) belongs to (Formula presented.) if, and only if, its support lies on (Formula presented.). 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. © 2016 World Scientific Publishing CompanyGiven a topological dynamical systems (X, T), consider a sequence of continuous potentials F := {fn : X → R}n≥1 that is asymptotically approached by sub-additive families. In a generalized version of ergodic optimization theory, one is interested in descr162CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - Conselho Nacional de Desenvolvimento Científico e Tecnológico306177/ 2011-0; 140675/ 2014-