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arXiv · 1207.2954

Epsilon-neighborhoods of orbits and formal classification of parabolic diffeomorphisms

Maja Resman
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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.

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Maja Resman. 2015-05-28. Epsilon-neighborhoods of orbits and formal classification of parabolic diffeomorphisms. https://arxiv.org/abs/1207.2954

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