Chain recurrence and average shadowing in dynamics

Autor(es)

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

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: MONATSHEFTE FUR MATHEMATIK; v. 196, n. 4 SEP 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático