Elismar R. Oliveira

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 Holder potential. Denote

Duality results for iterated function systems with a general family of branches

\displaystyle{m(A) =\max _{\nu \mbox{ an invariant probability for

General approach to conformal mappings used in atmospheric modeling

T

A Note on the Dynamics of Linear Automorphisms of a Convolution Measure Algebra

}}\int A(x)\;d\nu (x),}

Spectral radius ordering of starlike trees

and, μ ∞, A , any probability which attains the maximum value. We will assume that the maximizing probability μ ∞ is unique and has support in a periodic orbit. We denote by \(\mathbb{T}\) the left-shift acting on the space of points \((w,x) \in \{ 1,2,3,..,d\}^{\mathbb{Z}} =\varSigma \times \varSigma =\hat{\varSigma }\). For a given potential Holder \(A:\varSigma \rightarrow \mathbb{R}\), where A acts on the variable x, we say that a Holder continuous function \(W:\hat{\varSigma }\rightarrow \mathbb{R}\) is a involution kernel for A (where A ∗ acts on the variable w), if there is a Holder function \(A^{{\ast}}:\varSigma \rightarrow \mathbb{R}\), such that,

Ergodic transport theory and piecewise analytic subactions for analytic dynamics

\displaystyle{A^{{\ast}}(w) = A \circ \mathbb{T}^{-1}(w,x) + W \circ \mathbb{T}^{-1}(w,x) - W(w,x).}