Arithmetic progressions and chaos in linear dynamics

英文摘要：

We characterize chaotic linear operators on reflexive Banach spaces in terms of the existence of long arithmetic progressions in the sets of return times. To achieve this, we study $\mathcal F$-hypercyclicity for a family of subsets of the natural numbers associated with the existence of arbitrarily long arithmetic progressions. We investigate their connection with different concepts in linear dynamics.