The Dual Potential, the involution kernel and Transport in Ergodic Optimization

Artur O. Lopes, Elismar R. Oliveira, Philippe Thieullen

Consider the shift $\sigma$ acting on the Bernoulli space $\Sigma ={1,2,...,n}^{\mathbb{N}}$. We denote $\hat{\Sigma }={1,2,...,n}^{\mathbb{Z}}$. We analyze several properties of the maximizing probabil…