Bernardes-Junior, Nilson Da Costa; Caraballo, Blas M.; Darji, Udayan B.; Fávaro, Vinicius V.; Peris Manguillot, Alfredo(Elsevier, 2025-01-15)
[EN] We introduce and study the notions of (generalized) hyperbolicity, topological stability and (uniform) topological expansivity for operators on locally convex spaces. We prove that every generalized hyperbolic operator ...
[EN] In the present work we study the concepts of shadowing and chain recurrence in the setting of linear dynamics. We prove that shadowing and finite shadowing always coincide for operators on Banach spaces, but we exhibit ...
Bartoll Arnau, Salud; Martínez Jiménez, Félix; Peris Manguillot, Alfredo; Ródenas Escribá, Francisco De Asís(MDPI AG, 2022-12-15)
[EN] Let X be a compact metric space and a continuous map f:X-->X which defines a discrete dynamical system (X,f). The map f induces two natural maps, namely \bar{f}:K(X)-->K(X) on the hyperspace K(X) of non-empty compact ...
[EN] In this paper we introduce a concept of weak stability for non-autonomous dynamical systems. We characterize the set of weak stable points and show that the set of weak stable points is residual, and investigate the ...