A criterion for the positivity of the Liapunov characteristic exponent

1 December 1984

journal article
research article
Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems

Vol. 4 (4) , 527-539
https://doi.org/10.1017/s0143385700002625

Abstract

We formulate sufficient conditions under which, for a finite subset of SL (2, ℝ), the maximal Liapunov exponent is positive. These conditions are based on the notion of compatible hyperbolicity. We then give an analytical formulation of such a condition and we apply this criterion to prove mixing properties of a particular transformation of the two-dimensional torus.

Keywords

This publication has 3 references indexed in Scilit:

On the ergodic properties of piecewise linear perturbations of the twist map
Ergodic Theory and Dynamical Systems, 1982
A model problem with the coexistence of stochastic and integrable behaviour
Communications in Mathematical Physics, 1981
CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
Russian Mathematical Surveys, 1977