Jörg Schmeling, Bernd O. Stratmann
The Hausdorff Dimension of the Set of Dissipative Points for a Cantor--Like Model Set for Singly Cusped Parabolic Dynamics
Preprint series:
ESI preprints
- MSC:
- 60D05 Geometric probability, stochastic geometry, random sets, See also {52A22, 53C65}
- 14L35 Classical groups (geometric aspects), See also {20Gxx,
- 51N30 Geometry of classical groups, See also {20Gxx, 14L35}
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.
Keywords: fractal geometry, Hausdorff dimension, Cauchy random walks, Kleinian groups