Hölder continuous paths and hyperbolic toral automorphisms

Abstract

AbstractLet f:Tn→Tn (n ≥ 3) be a hyperbolic toral automorphism. Let A be the set of α > 0 such that there is a Hölder continuous path of index α in Tn with 1-dimensional orbit-closure under f We prove that α0 = sup A can be expressed in terms of the eigenvalues of f and that α0 ∈ A if and only if α0 < 1.