Dynamical self-similarity, L^q-dimensions and Furstenberg slicing in ℝ^d

2024/09/06 by Emilio Corso, Pablo Shmerkin, Corso, Emilio +1
Computer Science · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2409.04608

openalex publication_date 2024/09/06 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28

Abstract

We extend a theorem of the second author on the L^q-dimensions of dynamically driven self-similar measures from the real line to arbitrary dimension. Our approach provides a novel, simpler proof even in the one-dimensional case. As consequences, we show that, under mild separation conditions, the L^q-dimensions of homogeneous self-similar measures in ℝ^d take the expected values, and we derive higher rank slicing theorems in the spirit of Furstenberg's slicing conjecture.

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