Artículos de revistas
Shadowing and structural stability for operators
Fecha
2021-04-01Registro en:
Ergodic Theory and Dynamical Systems, v. 41, n. 4, p. 961-980, 2021.
1469-4417
0143-3857
10.1017/etds.2019.107
2-s2.0-85078036077
Autor
Universidade Federal do Rio de Janeiro (UFRJ)
Universidade Estadual Paulista (UNESP)
Institución
Resumen
A well-known result in the area of dynamical systems asserts that any invertible hyperbolic operator on any Banach space is structurally stable. This result was originally obtained by Hartman in 1960 for operators on finite-dimensional spaces. The general case was independently obtained by Palis and Pugh around 1968. We will exhibit a class of examples of structurally stable operators that are not hyperbolic, thereby showing that the converse of the above-mentioned result is false in general. We will also prove that an invertible operator on a Banach space is hyperbolic if and only if it is expansive and has the shadowing property. Moreover, we will show that if a structurally stable operator is expansive, then it must be uniformly expansive. Finally, we will characterize the weighted shifts on the spaces and (<![CDATA[1\leq p) that satisfy the shadowing property.