On non-uniformly 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 two which are at most finitely renormalizable and have only hyperbolic periodic points, as well as for all smooth interval maps with non-flat critical points.

21 pages

References in corpus (2)

• Local connectivity and quasi-conformal rigidity of non-renormalizable polynomials
• Non-uniform hyperbolicity in complex dynamics

Cited by in corpus (4)

• On stochastic stability of non-uniformly expanding interval maps
• Statistical properties of one-dimensional maps under weak hyperbolicity assumptions
• Nice inducing schemes and the thermodynamics of rational maps
• Large deviation principles of one-dimensional maps for Hölder continuous potentials