Formalisme thermodynamique
Group cohomology and the singularities of the Selberg zeta function associated to a Kleinian group.
Hard balls gas and Alexandrov spaces of curvature bounded above.
Hausdorff dimension of real numbers with bounded digit averages
Invariant measures for position dependent random maps with continuous random parameters
We consider a family of transformations with a random parameter and study a random dynamical system in which one transformation is randomly selected from the family and applied on each iteration. The parameter space may be of cardinality continuum. Further, the selection of the transformation need not be independent of the position in the state space. We show the existence of absolutely continuous invariant measures for random maps on an interval under some conditions.
Limit theorem for random walk in weakly dependent random scenery
Let S=(Sk)k≥0 be a random walk on ℤ and ξ=(ξi)i∈ℤ a stationary random sequence of centered random variables, independent of S. We consider a random walk in random scenery that is the sequence of random variables (Un)n≥0, where Un=∑k=0nξSk, n∈ℕ. Under a weak dependence assumption on the scenery ξ we prove a functional limit theorem generalizing Kesten and Spitzer’s [Z. Wahrsch. Verw. Gebiete50 (1979) 5–25] theorem.
Linear response for smooth deformations of generic nonuniformly hyperbolic unimodal maps
We consider families of unimodal maps whose critical point is slowly recurrent, and we show that the unique absolutely continuous invariant measure of depends differentiably on , as a distribution of order . The proof uses transfer operators on towers whose level boundaries are mollified via smooth cutoff functions, in order to avoid artificial discontinuities. We give a new representation of for a Benedicks-Carleson map , in terms of a single smooth function and the inverse branches...
Meromorphic extensions of generalised zeta functions.
Mertens theorem and closed orbits of ergodic toral automorphisms.
Moyenne de localisation fréquentielle des paquets d'ondelettes.
En utilisant le théorème de Ruelle d'opérateur de transfert, nous démontrons que la moyenne 2-k Σn=02k-1 ||^wn||L1 de la localisation fréquentielle pour les paquets d'ondelettes admet un équivalent de la forme cρk (c > 0, 1 < ρ < √2). Cela améliore une inégalité antérieurement obtenue par Coifman, Meyer et Wickerhauser. Des estimations numériques de ρ sont obtenues pour des filtres de Daubechies.
Nielsen fixed point theory and symplectic Floer homology
We describe a connection between Nielsen fixed point theory and symplectic Floer homology for surfaces. A new asymptotic invariant of symplectic origin is defined.
Nielsen number is a knot invariant
We show that the Nielsen number is a knot invariant via representation variety.
Nielsen zeta function, 3-manifolds, and asymptotic expansions in Nielsen theory.
On an analytic approach to the Fatou conjecture
Let f be a quadratic map (more generally, , d > 1) of the complex plane. We give sufficient conditions for f to have no measurable invariant linefields on its Julia set. We also prove that if the series converges absolutely, then its sum is non-zero. In the proof we use analytic tools, such as integral and transfer (Ruelle-type) operators and approximation theorems.
On an invariance principle for phase separation lines
On the rate of mixing of Axiom A flows.
Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature.
Poisson suspensions of compactly regenerative transformations
For infinite measure preserving transformations with a compact regeneration property we establish a central limit theorem for visits to good sets of finite measure by points from Poissonian ensembles. This extends classical results about (noninteracting) infinite particle systems driven by Markov chains to the realm of systems driven by weakly dependent processes generated by certain measure preserving transformations.
Puzzles of Quasi-Finite Type, Zeta Functions and Symbolic Dynamics for Multi-Dimensional Maps
Entropy-expanding transformations define a class of smooth dynamics generalizing interval maps with positive entropy and expanding maps. In this work, we build a symbolic representation of those dynamics in terms of puzzles (in Yoccoz’s sense), thus avoiding a connectedness condition, hard to satisfy in higher dimensions. Those puzzles are controled by a «constraint entropy» bounded by the hypersurface entropy of the aforementioned transformations.The analysis of those puzzles rests on a «stably...
Sector estimates for Kleinian groups.