Symbolic dynamics for one dimensional maps with nonuniform expansion

2018/01/10 by Yuri Lima, Lima, Yuri
Mathematics · Physics and Astronomy · #37B10 #37D25 #37E05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1801.03359

openalex publication_date 2018/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a piecewise C^1+β 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.

Citations

• Statistical Properties of Dynamical Systems with Some Hyperbolicity

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• Expanding Measures
• Symbolic dynamics for nonuniformly hyperbolic maps with singularities in high dimension
• Statistical stability of interval maps with critical points and singularities
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• Persistent Non-Statistical Dynamics in One-Dimensional Maps