In this paper we investigate the regularity of the topological entropy hto p for C k perturbations of Anosov flows. We show that the topological entropy varies (almost) as smoothly as theâ€¦ (More)

Let M be a Hadamard manifold of dimension 3 whose sectional curvature satisfies âˆ’b2 â‰¤ K â‰¤ âˆ’a2 < 0 and whose curvature tensor satisfies â€–âˆ‡Râ€– â‰¤ C for suitable constants 0 < a â‰¤ b and C â‰¥ 0. We showâ€¦ (More)

Topological and metric entropies are among the most important global invariants of smooth dynamical systems. Topological entropy characterizes the total exponential complexity of the orbit structureâ€¦ (More)

Let (M, g) be a compact Riemannian manifold with universal covering MÌƒ . The simplest asymptotic invariant which can be associated to (M, g) is the exponential growth rate h(g) of volume on theâ€¦ (More)

We show that there is a Câˆž open and dense set of positively curved metrics on S2 whose geodesic flow has positive topological entropy, and thus exhibits chaotic behavior. The geodesic flow for eachâ€¦ (More)

Long periodic orbits of hyperbolic dynamics do not exist as independent individuals but rather come in closely packed bunches. Under weak resolution a bunch looks like a single orbit in configurationâ€¦ (More)