We consider (M, d) a connected and compact manifold and we denote by the Bernoulli
space Mℤ. The analogous problem on the half-line ℕ is also considered. Let be an …

Let f be a real-valued function defined on the phase space of a dynamical system. Ergodic
optimization is the study of those orbits, or invariant probability measures, whose ergodic f …

Ergodic optimization is the study of problems relating to maximizing orbits and invariant
measures, and maximum ergodic averages. An orbit of a dynamical system is called a larger …

Entropy and variational principle for one-dimensional lattice systems with a general a priori
probability: positive and zero tem Page 1 Ergod. Th. & Dynam. Sys. (2015), 35, 1925–1961 …

Lecture notes of a course at the Brazilian Mathematical Colloquium. We review some basic
notions in ergodic theory and thermodynamic formalism, as well as introductory results in the …

We study the existence of solutions g to the functional inequality f≤ g∘ T− g+ β, where f is a
prescribed continuous function, T is a weakly expanding transformation of the circle having …

We introduce functions for relative maximization in a general context: the beta and alpha
applications. After a systematic study of different kinds of regularities, we investigate how to …

We show that there are examples of expansive, non-Anosov geodesic flows of compact
surfaces with non-positive curvature, where the Livsic Theorem holds in its classical …

Let T be the angle-doubling map on the circle T, and consider the 1-parameter family of
piecewise-linear cosine functions f_ θ: T → R, defined by f_ θ (x)= 1-4d_ T (x, θ). We identify …

Abstract Let T: X→ X be a dynamical system and &phis;: X→[special characters omitted] a
function on X. A function &thetas;: X→[special characters omitted] is called a sub-action for …