Rectifiability of a class of invariant measures with one non-vanishing Lyapunov exponent

2016/06/15 by Gabriel Fuhrmann, Jing Wang, Fuhrmann, Gabriel +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1606.04787

openalex publication_date 2016/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study order-preserving C¹-circle diffeomorphisms driven by irrational rotations with a Diophantine rotation number. We show that there is a non-empty open set of one-parameter families of such diffeomorphisms where the ergodic measures of nearly all family members are one-rectifiable, that is, absolutely continuous with respect to the restriction of the one-dimensional Hausdorff measure to a countable union of Lipschitz graphs.

Citations

• Some relations between dimension and Lyapounov exponents
• Dimension, entropy and Lyapunov exponents

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