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

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

2008-01-25

arxiv.org/abs/0801.3962v1

Mathematics

Dynamical Systems

Scientific paper

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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