The theory of random dynamical systems continues, extends, and unites various
developments in probability theory and dynamical systems. Roughly speaking, a random …

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 …

We consider the question of uniform convergence in the multiplicative ergodic theorem
[Formula: see text] for continuous function A: X→ GLd (R), where (X, T) is a uniquely ergodic …

We exhibit an explicit criterion for the simplicity of the Lyapunov spectrum of linear cocycles,
either locally constant or dominated, over hyperbolic (Axiom A) transformations. This …

Lyapunov exponents for some quasi-periodic cocycles Page 1 Ergod. Th. & Dynam. Sys. (1997),
17, 483–504 Printed in the United Kingdom c 1997 Cambridge University Press Lyapunov …

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 …

This book is devoted to the theory of topological dynamics of random dynamical systems.
The theory of random dynamical systems is a relatively new and fast expanding field of …

Continuity of Lyapunov exponents for random two-dimensional matrices Page 1 Ergod. Th. &
Dynam. Sys. (2017), 37, 1413–1442 doi:10.1017/etds.2015.116 c Cambridge University Press …

We prove an elementary formula about the average expansion of certain products of 2 by 2
matrices. This permits us to quickly re-obtain an inequality by M. Herman and a theorem by …

Let T be an aperiodic automorphism of a standard probability space (X, m). Let P be the
subset of A= L∞(X, Sl (2, R)) where the upper Lyapunov exponent is positive almost …