Self-similar fractals and common hypercyclicity

TL;DR

This paper generalizes a criterion for common hypercyclic vectors to higher dimensions, applying it to fractals and families of operators, notably products of backward shifts along H"older curves.

Contribution

It extends the Costakis-Sambarino criterion to multi-dimensional settings and fractals, enabling new applications in operator theory and fractal analysis.

Findings

Generalized the criterion for common hypercyclic vectors to higher dimensions.

Applied results to families of product operators parameterized by H"older curves.

Achieved optimal conditions for fractal-based operator families.

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 H\"older continuous curve in $\mathbb R^d$, for all $d\geq 1$.