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We consider the set of maps f 2 FC D( >C 1C of the circle which are covering maps of degree D, expanding, min x2S1f 0 .x/ > 1 and orientation preserving. We are interested in characterizing the set… (More)

We consider a specific example of a compact Riemannian surface M of genus 2 and constant negative curvature. We identify the boundary at infinity of M to the unit circle Σ=S1 and choose a particular… (More)

- Ph. Thieullen
- 1992

We define a sequence of uniform Lyapunov exponents in the setting of Banach spaces and prove that the Hausdorff dimension of global attractors is bounded from above by the Lyapunov dimension of the… (More)

AbstractLetfaa∈A be a C2 one-parameter family of non-flat unimodal maps of an interval into itself anda* a parameter value such that(a)fa* satisfies the Misiurewicz Condition,(b)fa* satisfies a… (More)

We propose a definition of topological stability for set-valued maps. We prove that a single-valued map which is topologically stable in the set-valued sense is topologically stable in the classical… (More)

L et(M, {φ t }) be a smooth (not necessarily transitive) Anosov flow without fixed points generated by a vector field X(x) = (d/dt)|t =0φ t (x) on a compact manifold M. Let A : M → R be a globally… (More)

In this mainly survey paper we consider the Lagrangian \( L(x,v) = \frac{1}{2} \, |v|^2 - V(x) \), and a closed form w on the torus \( \mathbb {T}^n \). For the associated Hamiltonian we consider the… (More)

- Ph. Thieullen
- 1997

We consider a random product of two-by-two matrices of determinant one over an abstract dynamical system. When the two Lyapunov exponents are distinct, Oseledets’ theorem asserts that the matrix… (More)

AbstractWe consider ergodic optimization for the shift map on the modified Bernoulli space σ: [0, 1]ℕ → [0, 1]ℕ, where [0, 1] is the unit closed interval, and the potential A: [0, 1]ℕ → ℝ considered… (More)

On a one-sided shift of finite type we prove that for a generic Holder continuous function there is a unique maximizing measure. We show that b-Holder continuous functions can be approximated in the… (More)