Generic points in systems of specification and Banach valued Birkhoff ergodic average

We prove that systems satisfying the specification property are saturated in the sense that the topological entropy of the set of generic points of any invariant measure is equal to the measure-theoretic entropy of the measure. We study Banach valued Birkhoff ergodic averages and obtain a variational principle for its topological entropy spectrum. As application, we examine a particular example concerning with the set of real numbers for which the frequencies of occurrences in their dyadic expansions of infinitely many words are prescribed. This relies on our explicit determination of a maximal entropy measure.Comment: accepted by Discrete and Continuous Dynamical System

Explicit fixed points of the smoothing transformation

We deal with the equation $Y \stackrel{\rm d}{=} \frac{1}{b} \sum_{1\le j\le N} W_jY_j$, where the unknown is the distribution of $Y$, the variables in the right hand side are independent, the $Y_j$ are equidistributed with $Y$, $N$ is an integer valued random variable, and the $W_j$ are equidistributed, nonnegative and of expectation~1. Usually a solution is obtained as the limit of a martingale. In some cases we give an explicit formula for the law of $Y$

IIAC – Centre d’études transdisciplinaires sociologie, anthropologie, histoire (CETSAH)

Daniel Friedmann, chargé de recherche au CNRSMonique Peyrière, ingénieure d’études à l’Université d’Evry Filmer le champ social Le séminaire a consisté notamment à analyser les questions d’ordre épistémologique que rencontre le chercheur qui s’essaie au langage filmique en tant que moyen de produire une recherche et qui rendent compte de ce que l’objectif de filmer le champ social a de problématique. Nous avons tout d’abord recensé les critiques philosophiques classiques d’inspiration platoni..