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

Abstract

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