2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146632In 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.Dynamical SystemsSpectral Theory60D05; 14L35; 51N30text