Espaces de Lebesgue
Sur la cohomologie dans les schémas de Bernoulli
We introduce an invariant of cohomology in Bernoulli shifts, which is used to answer a question about cohomology of Hölder functions with finitary functions whose coding time is integrable. When restricted to the class of Hölder functions, this invariant even provides a criterion of cohomology.
An extension which is relatively twofold mixing but not threefold mixing
We give an example of a dynamical system which is mixing relative to one of its factors, but for which relative mixing of order three does not hold.
Sur les processus quasi-Markoviens et certains de leurs facteurs
We study a class of stationary finite state processes, called quasi-Markovian, including in particular the processes whose law is a Gibbs measure as defined by Bowen. We show that, if a factor with integrable coding time of a quasi-Markovian process is maximal in entropy, then this factor splits off, which means that it admits a Bernoulli shift as an independent complement. If it is not maximal in entropy, then we can find a splitting finite extension of this factor, which generalizes a theorem...
L'ergodicité induit un type spectral maximal équivalent à la mesure de Lebesgue
Vitesse de dispersion pour une classe de martingales
The Pascal adic transformation is loosely Bernoulli
Zero Krengel entropy does not kill Poisson entropy
We prove that the notions of Krengel entropy and Poisson entropy for infinite-measure-preserving transformations do not always coincide: We construct a conservative infinite-measure-preserving transformation with zero Krengel entropy (the induced transformation on a set of measure 1 is the Von Neumann–Kakutani odometer), but whose associated Poisson suspension has positive entropy.
Almost-sure growth rate of generalized random Fibonacci sequences
We study the generalized random Fibonacci sequences defined by their first non-negative terms and for ≥1, +2= +1± (linear case) and +2=| +1± | (non-linear case), where each ± sign is independent and either + with probability or − with probability 1− (0<≤1). Our main result is that, when is of the form =2cos(/) for some integer ≥3, the exponential growth of for 0<≤1,...
Une transformation générique peut être insérée dans un flot
Examples and counterexamples to almost-sure convergence of bilateral martingales.
Weak mixing of maps with bounded cutting parameter.
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