Symbolic dynamics for one dimensional maps with nonuniform expansion

Abstract

Given a piecewise $C^{1+\beta }$ map of the interval, possibly with critical points and discontinuities, we construct a symbolic model for invariant probability measures with nonuniform expansion that do not approach the critical points and discontinuities exponentially fast almost surely. More specifically, we code the lift of these measures in the natural extension of the map.

arXiv comment33 pages, 1 figure, to appear in Annales de l'Institut Henri Poincaré / Analyse non linéaire

References in corpus (1)

• Lifting Measures to Inducing Schemes