The Hausdorff dimension of the set of dissipative points for a Cantor-like model set of singly cusped parabolic dynamics

Jörg Schmeling; Bernd Stratmann

doi:10.2996/kmj/1245982902

The Hausdorff dimension of the set of dissipative points for a Cantor-like model set of singly cusped parabolic dynamics

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Abstract

In this paper we introduce and study a certain intricate Cantor-like set C contained in unit interval. Our main result is to show that the set C itself, as well as the set of dissipative points within C, both have Hausdorff dimension equal to 1. The proof uses the transience of a certain non-symmetric Cauchy-type random walk.

Original language	English
Pages (from-to)	179-196
Journal	Kodai Mathematical Journal
Volume	32
Issue number	2
DOIs	https://doi.org/10.2996/kmj/1245982902
Publication status	Published - 2009

Subject classification (UKÄ)

Mathematical Sciences

Free keywords

Hausdorff dimension
Fractal geometry
Cauchy random walks
Kleinian
groups

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10.2996/kmj/1245982902

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title = "The Hausdorff dimension of the set of dissipative points for a Cantor-like model set of singly cusped parabolic dynamics",

abstract = "In this paper we introduce and study a certain intricate Cantor-like set C contained in unit interval. Our main result is to show that the set C itself, as well as the set of dissipative points within C, both have Hausdorff dimension equal to 1. The proof uses the transience of a certain non-symmetric Cauchy-type random walk.",

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AU - Stratmann, Bernd

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AB - In this paper we introduce and study a certain intricate Cantor-like set C contained in unit interval. Our main result is to show that the set C itself, as well as the set of dissipative points within C, both have Hausdorff dimension equal to 1. The proof uses the transience of a certain non-symmetric Cauchy-type random walk.

KW - Hausdorff dimension

KW - Fractal geometry

KW - Cauchy random walks

KW - Kleinian

KW - groups

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JO - Kodai Mathematical Journal

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The Hausdorff dimension of the set of dissipative points for a Cantor-like model set of singly cusped parabolic dynamics

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