| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Louisville, Dept Math, Louisville, KY 40292 - USA
[2] Univ Sao Paulo, Dept Computacao & Matemat, Fac Filosofia Ciencias & Letras, BR-14040901 Ribeirao Preto, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY; v. 64, n. 3, p. 513-531, AUG 2021. |
| Web of Science Citations: | 1 |
| Abstract | |
The notions of chaos and frequent hypercyclicity enjoy an intimate relationship in linear dynamics. Indeed, after a series of partial results, it was shown by Bayart and Ruzsa in 2015 that for backward weighted shifts on l(p)(Z), the notions of chaos and frequent hypercyclicity coincide. It is with some effort that one shows that these two notions are distinct. Bayart and Grivaux in 2007 constructed a non-chaotic frequently hypercyclic weighted shift on c(0). It was only in 2017 that Menet settled negatively whether every chaotic operator is frequently hypercylic. In this article, we show that for a large class of composition operators on L-p-spaces, the notions of chaos and frequent hypercyclicity coincide. Moreover, in this particular class, an invertible operator is frequently hypercyclic if and only if its inverse is frequently hypercyclic. This is in contrast to a very recent result of Menet where an invertible operator frequently hypercyclic on l(1) whose inverse is not frequently hypercyclic is constructed. (AU) | |
| FAPESP's process: | 18/06916-0 - Chaotic dynamical systems |
| Grantee: | Benito Frazao Pires |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 17/19360-8 - Topological dynamics of linear operators |
| Grantee: | Benito Frazao Pires |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 19/10269-3 - Ergodic and qualitative theories of dynamical systems II |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |