On non-uniform hyperbolicity assumptions in one-dimensional dynamics

Abstract

We give an essentially equivalent formulation of the backward contracting property, defined by Juan Rivera-Letelier, in terms of expansion along the orbits of critical values, for complex polynomials of degree at least 2 which are at most finitely renormalizable and have only hyperbolic periodic points, as well as all C3 interval maps with non-flat critical points. © 2010 Science China Press and Springer-Verlag Berlin Heidelberg.