Dimension bounds for invariant measures of bi-Lipschitz iterated\n function systems

2014/10/22 by Andreas Anckar, Anckar, Andreas
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1410.5927

openalex publication_date 2014/10/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We study probabilistic iterated function systems (IFS), consisting of a\nfinite or infinite number of average-contracting bi-Lipschitz maps on R^d. If\nour strong open set condition is also satisfied, we show that both upper and\nlower bounds for the Hausdorff and packing dimensions of the invariant measure\ncan be found. Both bounds take on the familiar form of ratio of entropy to the\nLyapunov exponent.\n

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