Quasi-shadowing for partially hyperbolic dynamics on Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:492

Article

Backes, Lucas¹  Dragicevic, Davor² 

[1] Univ Fed Rio Grande do Sul, Dept Matemat, Av Bento Goncalves 9500, BR-91509900 Porto Alegre, RS, Brazil

[2] Univ Rijeka, Dept Math, Rijeka, Croatia

关键词: Quasi-shadowing;    Nonautonomous systems;    Partial dichotomy;    Nonlinear perturbations;   

DOI  :  10.1016/j.jmaa.2020.124445

来源: Elsevier

【 摘 要 】

A partially hyperbolic dynamical system is said to have the quasi-shadowing property if every pseudotrajectory can be shadowed by a sequence of points (x(n))(n is an element of z) such that x(n+1) is obtained from the image of x(n) by moving it by a small factor in the central direction. In the present paper, we prove that a small nonlinear perturbation of a partially dichotomic sequence of (not necessarily invertible) linear operators acting on an arbitrary Banach space has the quasi-shadowing property. We also obtain a continuous time version of this result. As an application of our main result, we prove that a certain class of partially dichotomic sequences of linear operators is stable up to the movement in the central direction. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free