Berry–Esseen theorem and local limit theorem for non uniformly expanding maps
Beta-expansions with negative bases.
Bifurcations in One Dimension. I. The Nonwandering Set.
Bifurcations in One Dimension. II. A Versal Model for Bifurcations.
Billiard and diophantine approximation
Billiard complexity in the hypercube
We consider the billiard map in the hypercube of . We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that is the order of magnitude of the complexity.
Billiards: models with chaotic dynamics.
Binomial-Coefficient Multiples of Irrationals.
Birth of an elliptic island in a chaotic sea.
-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.