Absolutely Continuous Invariant Measures for Nonuniformly Expanding Maps

2005/10/25 by Huyi Hu, Sandro Vaienti, Hu, Huyi +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #advanced mathematical theories

paper · doi:10.48550/arxiv.math/0510527

openalex publication_date 2005/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a large class of nonuniformly expanding maps of \Bbb R^m, with indifferent fixed points and unbounded distorsion and non necessarily Markovian, we construct an absolutely continuous invariant measure. We extend to our case techniques previously used for expanding maps on quasi-Hölder spaces. We give general conditions and provide examples to which apply our result.

Citations

• Recurrence times and rates of mixing
• Statistical Properties of Dynamical Systems with Some Hyperbolicity

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