Product Recurrence for Weighted Backward Shifts

Authors

V?ctor J. Gal?n, Universidad Iberoamericana, Dominican RepublicFollow
Félix Mart?nez-Giménez, Universitat Polit`ecnica, Val`encia, SpainFollow
Piotr Oprocha, AGH University of Science and Technology, PolandFollow
Alfred Peris, Universitat Polit`ecnica, Val`encia, SpainFollow

Author Country (or Countries)

Spain

Abstract

We study product recurrence properties for weighted backward shifts on sequence spaces. The backward shifts that have non-zero product recurrent points are characterized as Devaney chaotic shifts. We also give an example of weighted shift that admits points which are recurrent and distal, but not product recurrent, in contrast with the dynamics on compact sets. An example of a product recurrent point with unbounded orbit is also provided.

Recommended Citation

J. Gal?n, V?ctor; Mart?nez-Giménez, Félix; Oprocha, Piotr; and Peris, Alfred (2023) "Product Recurrence for Weighted Backward Shifts," Applied Mathematics & Information Sciences: Vol. 09: Iss. 5, Article 18.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss5/18