Kodai Mathematical Journal

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

Jörg Schmeling and Bernd O. Stratmann

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Abstract

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

Article information

Source
Kodai Math. J. Volume 32, Number 2 (2009), 179-196.

Dates
First available in Project Euclid: 26 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1245982902

Digital Object Identifier
doi:10.2996/kmj/1245982902

Mathematical Reviews number (MathSciNet)
MR2549541

Zentralblatt MATH identifier
1183.28016

Citation

Schmeling, Jörg; Stratmann, Bernd O. The Hausdorff dimension of the set of dissipative points for a Cantor-like model set for singly cusped parabolic dynamics. Kodai Math. J. 32 (2009), no. 2, 179--196. doi:10.2996/kmj/1245982902. https://projecteuclid.org/euclid.kmj/1245982902.


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