Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899882 | Journal of Mathematical Analysis and Applications | 2018 | 12 Pages |
Abstract
We prove that a bounded operator T on a separable Banach space X satisfying a strong form of the Frequent Hypercyclicity Criterion (which implies in particular that the operator is universal in the sense of Glasner and Weiss) admits frequently hypercyclic vectors with irregularly visiting orbits, i.e. vectors xâX such that the set NT(x,U)={nâ¥1;TnxâU} of return times of x into U under the action of T has positive lower density for every non-empty open set UâX, but there exists a non-empty open set U0âX such that NT(x,U0) has no density.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
S. Grivaux,