Naslov
Shadowing for nonautonomous dynamics

Autori
Backes, Lucas ; Dragičević, Davor.

Izvornik
Advanced nonlinear studies (1536-1365) 19 (2019), 2; 425-436

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

Ključne riječi
Shadowing, Nonautonomus systems, Exponential dichotomies, Nonlinear perturbations.

Sažetak
We prove that whenever a sequence of invertible and bounded operators (Am)m∈Z acting on a Banach space X admits an exponential dichotomy and a sequence of differentiable maps fm : X → X, m ∈ Z, has bounded and H¨older derivatives, the nonautonomous dynamics given by xm+1 = Amxm + fm(xm), m ∈ Z has various shadowing properties. Hence, we extend recent results of Bernardes Jr. et al. in several directions. As a nontrivial application of our results, we give a new proof of the nonautonomous Grobman- Hartman theorem.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA