Symbolic dynamics for one dimensional maps with nonuniform expansion

摘要

Given a piecewise C1+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, for each chi > 0 we construct a finite-to-one Holder continuous map from a countable topological Markov shift to the natural extension of the interval map, that codes the lifts of all invariant probability measures as above with Lyapunov exponent greater than chi almost everywhere. (C) 2019 Elsevier Masson SAS. All rights reserved.