Parameter dependence of stable manifolds under nonuniform hyperbolicity

Stable Manifolds under Very Weak Hyperbolicity Conditions

We present an argument for proving the existence of local stable and unstable manifolds in a general abstract setting and under very weak hyperbolicity conditions.

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Horospheres and hyperbolicity of Hadamard manifolds

Article history: Available online 4 March 2014 Communicated by O. Kowalski MSC: primary 53C20 secondary 32Q05, 53C40, 53C25

On the Work of Dolgopyat on Partial and Nonuniform Hyperbolicity

The paper is a non-technical survey and is aimed to illustrate Dolgopyat’s profound contributions to smooth ergodic theory. I will discuss some of Dolgopyat’s work on partial hyperbolicity and nonuniform hyperbolicity with emphasis on interaction between the two – the class of dynamical systems with mixed hyperbolicity. On the one hand, this includes uniformly partially hyperbolic diffeomorphis...

Reducibility or nonuniform hyperbolicity for quasiperiodic Schrödinger cocycles

We show that for almost every frequency α ∈ R\Q, for every Cω potential v : R/Z → R, and for almost every energy E the corresponding quasiperiodic Schrödinger cocycle is either reducible or nonuniformly hyperbolic. This result gives very good control on the absolutely continuous part of the spectrum of the corresponding quasiperiodic Schrödinger operator, and allows us to complete the proof of ...