Naslov
Quasi-shadowing for partially hyperbolic dynamics on Banach spaces

Autori
Backes, Lucas ; Dragičević, Davor

Izvornik
Journal of mathematical analysis and applications (0022-247X) 492 (2020), 1; 124445, 18

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Quasi-shadowing, Nonautonomus systems ; Partial dichotomy ; Nonlinear perturbations

Sažetak
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\in \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 get 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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