Invariant manifolds and cluster synchronization in a family of locally coupled map lattices.
Invariant manifolds associated to invariant subspaces without invariant complements: a graph transform approach.
Invariant Measures and Minimal Sets of Horospherical Flows.
Invariant measures exist under a summability condition for unimodal maps.
Invariant measures for a diffeomorphism which expands the leaves of a foliation
Invariant measures for the stable foliation on negatively curved periodic manifolds
We classify reversible measures for the stable foliation on manifolds which are infinite covers of compact negatively curved manifolds. We extend the known results from hyperbolic surfaces to varying curvature and to all dimensions.
Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds
Invariant scrambled sets and maximal distributional chaos
For the full shift (Σ₂,σ) on two symbols, we construct an invariant distributionally ϵ-scrambled set for all 0 < ϵ < diam Σ₂ in which each point is transitive, but not weakly almost periodic.
Invariant Sets of Anosovs Diffeomorphisms.
Invariant sets with zero measure and full Hausdorff dimension.
Invariant two-forms for geodesic flows.
Invariants of twist-wise flow equivalence.
Isomorphism of regular Morse dynamical systems induced by arbitrary blocks
Khinchin type condition for translation surfaces and asymptotic laws for the Teichmüller flow
We study a diophantine property for translation surfaces, defined in terms of saddle connections and inspired by classical Khinchin condition. We prove that the same dichotomy holds as in Khinchin theorem, then we deduce a sharp estimate on how fast the typical Teichmüller geodesic wanders towards infinity in the moduli space of translation surfaces. Finally we prove some stronger result in genus one.
Kneading sequences of skew tent maps
Knots on a positive template have a bounded number of prime factors.
La condition de Walters
Labeled Rauzy classes and framed translation surfaces
In this paper, we compare two definitions of Rauzy classes. The first one was introduced by Rauzy and was in particular used by Veech to prove the ergodicity of the Teichmüller flow. The second one is more recent and uses a “labeling” of the underlying intervals, and was used in the proof of some recent major results about the Teichmüller flow.The Rauzy diagrams obtained from the second definition are coverings of the initial ones. In this paper, we give a formula that gives the degree of this covering.This...
Large deviation asymptotics for Anosov flows
Large deviations, Gibbs measures and closed orbits for hyperbolic flows.