-continuity of the Fröbenius-Perron semigroup.
Cardinality of Rauzy classes
Rauzy classes form a partition of the set of irreducible permutations. They were introduced as part of a renormalization algorithm for interval exchange transformations. We prove an explicit formula for the cardinality of each Rauzy class. Our proof uses a geometric interpretation of permutations and Rauzy classes in terms of translation surfaces and moduli spaces.
Central limit theorems for non-invertible measure preserving maps
Using the Perron-Frobenius operator we establish a new functional central limit theorem for non-invertible measure preserving maps that are not necessarily ergodic. We apply the result to asymptotically periodic transformations and give a specific example using the tent map.
Chaotic dynamics and nonlinear feedback control
Chaotic hypothesis and universal large deviations properties.
Characterizing mildly mixing actions by orbit equivalence of products.
Closed orbits in homology classes
Codages de rotations et phénomènes d'autosimilarité
Nous étudions une classe de suites symboliques, les codages de rotations, intervenant dans des problèmes de répartition des suites et représentant une généralisation géométrique des suites sturmiennes. Nous montrons que ces suites peuvent être obtenues par itération de quatre substitutions définies sur un alphabet à trois lettres, puis en appliquant un morphisme de projection. L’ordre d’itération de ces applications est gouverné par un développement bi-dimensionnel de type “fraction continue”...
Combinatoire du billard dans un polyèdre
Ces notes ont pour but de rassembler les différents résultats de combinatoire des mots relatifs au billard polygonal et polyédral. On commence par rappeler quelques notions de combinatoire, puis on définit le billard, les notions utiles en dynamique et le codage de l’application. On énonce alors les résultats connus en dimension deux puis trois.
Complete positivity of entropy and non-Bernoullicity for transformation groups
The existence of non-Bernoullian actions with completely positive entropy is proved for a class of countable amenable groups which includes, in particular, a class of Abelian groups and groups with non-trivial finite subgroups. For this purpose, we apply a reverse version of the Rudolph-Weiss theorem.
Completely mixing maps without limit measure
We combine some results from the literature to give examples of completely mixing interval maps without limit measure.
Conformal measures for rational functions revisited
We show that the set of conical points of a rational function of the Riemann sphere supports at most one conformal measure. We then study the problem of existence of such measures and their ergodic properties by constructing Markov partitions on increasing subsets of sets of conical points and by applying ideas of the thermodynamic formalism.
Conjugacies between ergodic transformations and their inverses
We study certain symmetries that arise when automorphisms S and T defined on a Lebesgue probability space (X, ℱ, μ) satisfy the equation . In an earlier paper [6] it was shown that this puts certain constraints on the spectrum of T. Here we show that it also forces constraints on the spectrum of . In particular, has to have a multiplicity function which only takes even values on the orthogonal complement of the subspace . For S and T ergodic satisfying this equation further constraints arise,...
Connectedness of fractals associated with Arnoux–Rauzy substitutions
Rauzy fractals are compact sets with fractal boundary that can be associated with any unimodular Pisot irreducible substitution. These fractals can be defined as the Hausdorff limit of a sequence of compact sets, where each set is a renormalized projection of a finite union of faces of unit cubes. We exploit this combinatorial definition to prove the connectedness of the Rauzy fractal associated with any finite product of three-letter Arnoux–Rauzy substitutions.
Consistency of the LSE in Linear regression with stationary noise
We obtain conditions for L₂ and strong consistency of the least square estimators of the coefficients in a multi-linear regression model with a stationary random noise. For given non-random regressors, we obtain conditions which ensure L₂-consistency for all wide sense stationary noise sequences with spectral measure in a given class. The condition for the class of all noises with continuous (i.e., atomless) spectral measures yields also -consistency when the noise is strict sense stationary with...
Constructing complete chaotic maps with reciprocal structures.
Constructing equivariant maps for representations
We show that if is a discrete subgroup of the group of the isometries of , and if is a representation of into the group of the isometries of , then any -equivariant map extends to the boundary in a weak sense in the setting of Borel measures. As a consequence of this fact, we obtain an extension of a result of Besson, Courtois and Gallot about the existence of volume non-increasing, equivariant maps. Then, we show that the weak extension we obtain is actually a measurable -equivariant...
Construction de cocycles en escalier ergodiques et faiblement mélangeants au-dessus de rotations irrationnelles du cercle
Construction of 0-1 matrices associated to period-doubling processes.
We elaborate a method allowing the determination of 0-1 matrices corresponding to dynamics of the interval having stable, 2k-periodic orbits, k belonging to N. By recurrence on the finite dimensional matrices, we establish the form of the infinite matrices (k --> ∞).
Construction of curious minimal uniquely ergodic homeomorphisms on manifolds : the Denjoy–Rees technique