Corrigendum to the paper "Semigroup actions on tori and stationary measures on projective spaces" (Studia Math. 171 (2005), 33-66)
Counting and convergence in ergodic theory
Coupled maps and analytic function spaces
Courants ergodiques et répartition géométrique.
Decay of correlations for non Hölderian dynamics. A coupling approach.
Decay of correlations for nonuniformly expanding systems
We estimate the speed of decay of correlations for general nonuniformly expanding dynamical systems, using estimates on the time the system takes to become really expanding. Our method can deal with fast decays, such as exponential or stretched exponential. We prove in particular that the correlations of the Alves-Viana map decay in .
Decay of correlations in one-dimensional dynamics
Dense orbits of horospherical flows
Densité des orbites des trajectoires browniennes sous l’action de la transformation de Lévy
Let Tbe a measurable transformation of a probability space , preserving the measureπ. Let X be a random variable with law π. Call K(⋅, ⋅) a regular version of the conditional law of X given T(X). Fix . We first prove that ifB is reachable from π-almost every point for a Markov chain of kernel K, then the T-orbit of π-almost every point X visits B. We then apply this result to the Lévy transform, which transforms the Brownian motion W into the Brownian motion |W| − L, where L is the local time...
Density estimation for one-dimensional dynamical systems
In this paper we prove a Central Limit Theorem for standard kernel estimates of the invariant density of one-dimensional dynamical systems. The two main steps of the proof of this theorem are the following: the study of rate of convergence for the variance of the estimator and a variation on the Lindeberg–Rio method. We also give an extension in the case of weakly dependent sequences in a sense introduced by Doukhan and Louhichi.
Density Estimation for One-Dimensional Dynamical Systems
In this paper we prove a Central Limit Theorem for standard kernel estimates of the invariant density of one-dimensional dynamical systems. The two main steps of the proof of this theorem are the following: the study of rate of convergence for the variance of the estimator and a variation on the Lindeberg–Rio method. We also give an extension in the case of weakly dependent sequences in a sense introduced by Doukhan and Louhichi.
Density of paths of iterated Lévy transforms of brownian motion
The Lévy transform of a Brownian motion B is the Brownian motion B(1) given by Bt(1) = ∫0tsgn(Bs)dBs; call B(n) the Brownian motion obtained from B by iterating n times this transformation. We establish that almost surely, the sequence of paths (t → Bt(n))n⩾0 is dense in Wiener space, for the topology of uniform convergence on compact time intervals.
Density of paths of iterated Lévy transforms of Brownian motion
The Lévy transform of a Brownian motion B is the Brownian motion B(1) given by Bt(1) = ∫0tsgn(Bs)dBs; call B(n) the Brownian motion obtained from B by iterating n times this transformation. We establish that almost surely, the sequence of paths (t → Bt(n))n⩾0 is dense in Wiener space, for the topology of uniform convergence on compact time intervals.
Density of periodic orbit measures for transformations on the interval with two monotonic pieces
Transformations T:[0,1] → [0,1] with two monotonic pieces are considered. Under the assumption that T is topologically transitive and , it is proved that the invariant measures concentrated on periodic orbits are dense in the set of all invariant probability measures.
Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits
Let K be the Cantor set. We prove that arbitrarily close to a homeomorphism T: K → K there exists a homeomorphism T̃: K → K such that the ω-limit of every orbit is a periodic orbit. We also prove that arbitrarily close to an endomorphism T: K → K there exists an endomorphism T̃: K → K with every orbit finally periodic.
Derivatives of circle rotations, and similarity of orbits.
Deux caractérisations de la mesure d’équilibre d’un endomorphisme de
Soit µ la mesure d’équilibre d’un endomorphisme de . Nous montrons ici qu’elle est son unique mesure d’entropie maximale. Nous construisons directement µ comme distribution asymptotique des préimages
Deux caractérisations de la mesure d’équilibre d’un endomorphisme de P k (C)
Développement en base , répartition modulo un de la suite , n, langages codés et -shift
Déviations de moyennes ergodiques, flots de Teichmüller et cocycle de Kontsevich-Zorich
Étant donnée une fonction régulière de moyenne nulle sur le tore de dimension , il est facile de voir que ses intégrales ergodiques au-dessus d’un flot de translation “générique”sont bornées. Il y a une dizaine d’années, A. Zorich a observé numériquement une croissance en puissance du temps de ces intégrales ergodiques au-dessus de flots d’hamiltoniens (non-exacts) “génériques”sur des surfaces de genre supérieur ou égal à , et Kontsevich et Zorich ont proposé une explication (conjecturelle) de...