In broad terms, the goal of dynamics is to describe the long-term evolution of systems for
which an" infinitesimal" evolution rule, such as a differential equation or the iteration of a …

Abstract We prove the Zorich–Kontsevich conjecture that the non-trivial Lyapunov exponents
of the Teichmüller ow on (any connected component of a stratum of) the moduli space of …

We propose a new approach to analyzing dynamical systems that combine hyperbolic and
non-hyperbolic (“center”) behavior, eg partially hyperbolic diffeomorphisms. A number of …

We prove that for any s> 0 the majority of C^s linear cocycles over any hyperbolic (uniformly
or not) ergodic transformation exhibit some nonzero Lyapunov exponent: this is true for an …

Let V=R^d be the Euclidean d-dimensional space, μ (resp. λ) a probability measure on the
linear (resp. affine) group G=GL(V) (resp. H=Aff(V)) and assume that μ is the projection of λ …

We consider finite families of SL (2, ℝ) matrices whose products display uniform exponential
growth. These form open subsets of (SL (2, ℝ)) N, and we study their components, boundary …

In an explicit family of partially hyperbolic diffeomorphisms of the torus T3, Shub and
Wilkinson recently succeeded in perturbing the Lyapunov exponents of the center direction …

We consider volume-preserving perturbations of the time-one map of the geodesic flow of a
compact surface with negative curvature. We show that if the Liouville measure has …

We consider a large class of 2D area-preserving diffeomorphisms that are not uniformly
hyperbolic but have strong hyperbolicity properties on large regions of their phase spaces. A …

We consider random products of SL (2, R) matrices that depend on a parameter in a non-
uniformly hyperbolic regime. We show that if the dependence on the parameter is monotone …