Chain recurrence and average shadowing in dynamics

Author(s)

Alves, Fabricio F. ^[1] ; Bernardes Jr, Nilson C. ; Messaoudi, Ali ^[2]

Affiliation

^[1] Inst Fed Educ Ciencia & Tecnol Sao Paulo, Campus Presidente Epitacio, Rua Jose Ramos Jr, BR-19470000 Presidente Epitacio, SP - Brazil

^[2] Univ Estadual Paulista, Dept Matemat, Rua Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

• Document type: Journal article
• Source: MONATSHEFTE FUR MATHEMATIK; v. 196, n. 4 SEP 2021.
• Web of Science Citations: 0

Abstract

We investigate several notions related to pseudotrajectories, including chain recurrence and shadowing properties, for a special class of diffeomorphisms on euclidean spheres, known as spherical linear transformations, and for bounded linear operators on Banach spaces. Our main results are complete characterizations of chain recurrence for spherical linear transformations on euclidean spheres and for weighted shifts on the classical Banach sequence spaces c(0) and l(p). Another main result is a characterization of hyperbolicity for invertible operators on Banach spaces by means of average expansivity and the average shadowing property. (AU)

• FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
• Grantee: Claudio Aguinaldo Buzzi
• Support Opportunities: Research Projects - Thematic Grants