Mauduit and SÃ¡rkÃ¶zy introduced and studied certain numerical parameters associated to finite binary sequences EN âˆˆ {âˆ’1, 1}N in order to measure their â€˜level of randomnessâ€™. Those parameters, theâ€¦ (More)

Mauduit and SÃ¡rkÃ¶zy introduced and studied certain numerical parameters associated to finite binary sequences EN âˆˆ {âˆ’1, 1} in order to measure their â€˜level of randomnessâ€™. These parameters, theâ€¦ (More)

We prove that almost every nonregular real quadratic map is ColletEckmann and has polynomial recurrence of the critical orbit (proving a conjecture by Sinai). It follows that typical quadratic mapsâ€¦ (More)

We review recent results that lead to a very precise understanding of the dynamics of typical unimodal maps from the statistical point of view. We also describe the (generalized) renormalizationâ€¦ (More)

We prove that there is a residual set of families of smooth or analytic unimodal maps with quadratic critical point and negative Schwarzian derivative such that almost every parameter is eitherâ€¦ (More)

We obtain estimates relating the phase space and the parameter space of analytic families of unimodal maps. Using those estimates, we show that typical analytic unimodal maps admit a quasiquadraticâ€¦ (More)

Consider deterministic random walks F : I Ã— Z â†’ I Ã— Z, defined by F (x, n) = (f(x), Ïˆ(x) + n), where f is an expanding Markov map on the interval I and Ïˆ : I â†’ Z. We study the universalityâ€¦ (More)

The goal of this paper is to introduce methods that allow one to obtain continuous-time versions of various discrete-time ergodic results. While the classical von Neumannâ€™s and Birkhoffâ€™s ergodicâ€¦ (More)

The complexity function of an infinite word w on a finite alphabet A is the sequence counting, for each nonnegative n, the number of words of lenght n on the alphabet A that are factors of theâ€¦ (More)