Higher-dimensional multifractal analysis for the cusp winding process on hyperbolic surfaces

2024/02/26 by Yuya Arima, Arima, Yuya · 2 citations
Engineering · #Dynamical Systems (math.DS) #FOS: Mathematics #Material Properties and Processing #Number Theory (math.NT) #Tribology and Lubrication Engineering #Vibration and Dynamic Analysis

paper · pdf · doi:10.48550/arxiv.2402.16418

openalex publication_date 2024/02/26 · openalex created_date 2024/02/28 · openalex updated_date 2026/07/28

Abstract

We perform a multifractal analysis of the growth rate of the number of cusp windings for the geodesic flow on hyperbolic surfaces with m ≥ 1 cusps. Our main theorem establishes a conditional variational principle for the Hausdorff dimension spectrum of the multi-cusp winding process. Moreover, we show that the dimension spectrum defined on ℝ_>0^m is real analytic. To prove the main theorem we use a countable Markov shift with a finitely primitive transition matrix and thermodynamic formalism.

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• Thermodynamic formalism and multifractal analysis of Birkhoff averages for non-uniformly expanding Rényi interval maps with countably many branches
• Thermodynamic formalism and multifractal analysis of Birkhoff averages for non-uniformly expanding interval maps with finitely many branches

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