Naslov
Asymptotic stability of nonuniform behaviour

Autori
Dragičević, Davor ; Zhang, Weinian

Izvornik
Proceedings of the American Mathematical Society (0002-9939) 147 (2019), 6; 2437-2451

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

Ključne riječi
nonuniform exponential dichotomy, roughness

Sažetak
This paper is devoted to exponential dichotomies of nonautonomous difference equations. Under the assumptions that $(A_m)_{; ; ; ; m\in \Z}; ; ; ; $ is a sequence of bounded operators acting on an arbitrary Banach space $X$ that admits a uniform exponential dichotomy and that $(B_m)_{; ; ; ; m\in \Z}; ; ; ; $ is a sequence of compact operators such that $\lim_{; ; ; ; \lvert m\rvert \to \infty}; ; ; ; \lVert B_m\rVert=0$, D. Henry proved that either the sequence $(A_m+B_m)_{; ; ; ; m\in \Z}; ; ; ; $ admits a uniform exponential dichotomy or there exists a bounded nonzero sequence $(x_m)_{; ; ; ; m\in \Z}; ; ; ; \subset X$ such that $x_{; ; ; ; m+1}; ; ; ; = (A_m+B_m)x_m$ for each $m\in \Z$. In this paper we prove Henry's result in the setting of \emph{; ; ; ; nonuniform}; ; ; ; exponential dichotomies. Then we obtain a result on roughness of the nonuniform exponential dichotomy and give stability of Lyapunov exponents. In addition, we establish corresponding results for dynamics with continuous time.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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