INTERMEDIATE LYAPUNOV EXPONENTS FOR SYSTEMS WITH PERIODIC ORBIT GLUING PROPERTY

摘要

We prove that the average Lyapunov exponents of asymptotically additive functions have the intermediate value property provided the dynamical system has the periodic gluing orbit property. To be precise, consider a continuous map f : X - X over a compact metric space X and an asymp- totically additive sequence of functions Phi = {phi(n) : X - R}(n = 1). If f has the periodic gluing orbit property, then for any constant a satisfyinginf(mu is an element of Minv(f,X)) chi Phi(mu) a sup (mu is an element of Minv(f,X)) chi Phi(mu)where chi Phi(mu) = lim inf(n -infinity) integral 1 phi(n)d mu, and the infimum and supremum are taken over the set of all f-invariant probability measures, there is an ergodic measure it mu(a) is an element of M-inv (f, X) such that chi Phi(mu(a)) = a and supp(mu) = X.