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

Kodai Mathematical Journal

Jörg Schmeling¹  Bernd O. Stratmann² 

[1] Department of Mathematics, LTH University of Lund;Mathematical Institute University of St. Andrews

关键词: Fractal geometry;    Hausdorff dimension;    Cauchy random walks;    Kleinian groups;   

DOI  :  10.2996/kmj/1245982902

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(17)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.

【 授权许可】

Unknown