We consider random walks on Z in a stationary random medium, defined by an ergodic dynamical system, in the case when the possible jumps are {−L, . . . ,−1,0,+1} for some fixed integer L. We provide… (More)

We consider a one-dimensional random walk with bounded steps in a stationary and ergodic random medium. We the algebraic structure of the random walk is given by geometrical invariants related to the… (More)

We study injective locally contracting maps of the Interval. After giving an upper-bound on the number of ergodic components, we show that generically finitely many periodic orbits attract the whole… (More)

Given the Circle endowed with the doubling map, we consider the problem of maximizing measures for Lipschitz functions. We provide a reduction result for the conjecture stating that in a dense open… (More)

We consider a model of random walks on Z with finite range in a stationary and ergodic random environment. We first provide a fine analysis of the geometrical properties of the central left and right… (More)

We consider Davenport-like series with coefficients in l and discuss L-convergence as well as almost-everywhere convergence. We give an example where both fail to hold. We next improve former… (More)

Above an irrational rotation on the Circle, we build optimally smooth ergodic cocycles with values in some nilpotent or solvable subgroups of triangular matrices.

Let M(T1, T ) be the convex set of Borel probability measures on the Circle T invariant under the action of the transformation T : x 7−→ 2x mod (1). Its projection on the complex plane by the… (More)

In the natural context of ergodic optimization, we provide a short proof of the assertion that the maximizing measure of a generic continuous function has zero entropy. Abstract Dans le cadre usuel… (More)

We consider a one-dimensional random walk with finite range in a random medium described by an ergodic translation on a torus. For regular data and under a Diophantine condition on the translation we… (More)