Existence of Periodic Points of Maps of S1.
Expanding attractors
Expansive homeomorphisms and indecomposability
Expansiveness on Compact Piecewise Linear Manifolds.
Fibrés dynamiques. Entropie et dimension
First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity
Flots d'Anosov à distributions de Liapounov différentiables. I
Flots d'Anosov sur les variétés graphées au sens de Waldhausen
Cet article est consacré à l’étude d’une large classe de flots d’Anosov sur les variétés graphées. Nous établissons un résultat général à propos des plongements de variétés de Seifert dans les variétés de dimension 3 admettant un flot d’Anosov produit, généralisant ainsi un résultat de E. Ghys. Nous montrons que, à isotopie près, la restriction du feuilletage unidimensionnel défini par le flot à l’image de ce plongement est topologiquement conjugué à un morceau de flot géodésique privé d’un nombre...
Frame flows on manifolds with pinched negative curvature
Géométrie des variétés invariantes d'un difféomorphisme axiome A et transversalité forte
Holomorphic Anosov systems.
Homoclinic Points in Conservative Systems.
Horospheres and the Stable Part of the Geodesic Flow.
Hyperbolic dynamics of Euler-Lagrange flows on prescribed energy levels
Hyperbolic homeomorphisms and bishadowing
Hyperbolic homeomorphisms on compact manifolds are shown to have both inverse shadowing and bishadowing properties with respect to a class of δ-methods which are represented by continuous mappings from the manifold into the space of bi-infinite sequences in the manifold with the product topology. Topologically stable homeomorphisms and expanding mappings are also considered.
Hyperbolicity in a class of one-dimensional maps.
In this paper we provide a direct proof of hyperbolicity for a class of one-dimensional maps on the unit interval. The maps studied are degenerate forms of the standard quadratic map on the interval. These maps are important in understanding the Newhouse theory of infinitely many sinks due to homoclinic tangencies in two dimensions.
Hyperbolicity, stability, and the criterion of homoclinic points.
Induced expansion for quadratic polynomials
Inflationary tilings with a similarity structure.
Invariant densities for C¹ maps
We consider the set of expanding maps of the circle which have a unique absolutely continuous invariant probability measure whose density is unbounded, and show that this set is dense in the space of expanding maps with the topology. This is in contrast with results for or maps, where the invariant densities can be shown to be continuous.