Ergodic Transport Theory, Periodic Maximizing Probabilities and the Twist Condition
Ergodic Transport Theory, Periodic Maximizing Probabilities and the Twist Condition
Consider the shift T acting on the Bernoulli space $$\varSigma =\{ 1,2,3,..,d\}^{\mathbb{N}}$$ and $$A:\varSigma \rightarrow \mathbb{R}$$ a Hölder potential. Denote $$\displaystyle{m(A) =\max _{\nu \mbox{ an invariant probability for $T$}}\int A(x)\;d\nu (x),}$$ and, μ ∞, A , any probability which attains the maximum value. We will assume that the maximizing probability …