Self-similar fractals and common hypercyclicity

Abstract

We obtain a multi-dimensional generalization of the Costakis-Sambarino criterion for common hypercyclic vectors with optimal consequences on a large class of fractals. Applications include families of products of backward shifts parameterized by any Hölder continuous curve in ${\mathbb{R}}^d$, for all $d\ge 1$.

42 pages, 14 figures

References in corpus (2)

• Common hypercyclic vectors for composition operators
• Space-filling curves of self-similar sets (I): Iterated function systems with order structure