Epsilon-neighborhoods of orbits and formal classification of parabolic diffeomorphisms

2012/07/12 by Maja Resman, Resman, Maja · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #28A75 #28A78 #37C05 #37C10 #37C15 #37C25 #Advanced Mathematical Theories and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Fractal and DNA sequence analysis #Mathematical Dynamics and Fractals #math.DS #msc:28A75 #msc:28A78 #msc:37C05 #msc:37C10 #msc:37C15 #msc:37C25

paper · pdf · doi:10.48550/arxiv.1207.2954

25 pages, 2 figures

openalex publication_date 2012/07/12 · arxiv created 2015/05/28 · arxiv updated 2015/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we study the dynamics generated by germs of parabolic diffeomorphisms f : (C; 0)->(C; 0) tangent to the identity. We show how formal classification of a given parabolic diffeomorphism can be deduced from the asymptotic development of what we call directed area of the epsilon-neighborhood of any orbit near the origin. Relevant coefficients and constants in the development have a geometric meaning. They present fractal properties of the orbit, namely its box dimension, Minkowski content and what we call residual content.

Citations

• Fractal Geometry: Mathematical Foundations and Applications.

Cited by

• Support measures in fractal geometry

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