Hausdorff dimension and hierarchical system dynamics

2009/06/08 by K. Lukierska‐Walasek, K. Lukierska-Walasek, Lukierska-Walasek, K. +3
Computer Science · Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Statistical Mechanics (cond-mat.stat-mech) #Topological and Geometric Data Analysis #advanced mathematical theories #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.0906.1486

7 pages

arxiv created 2009/06/08 · openalex publication_date 2009/06/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that Hausdorff dimension may be used to distinguish different dynamics of therelaxation in hierarchical systems. We examine the hierarchical systems following the temperature-dependent power-law decay and the Kohlrausch law. For our purposes, we consider a Lévy stochastic processes on p-adic integer numbers.

Citations

• Some theorems on stable processes

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