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.