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ASYMPTOTIC STABILITY OF NONUNIFORM BEHAVIOUR.
- Source :
-
Proceedings of the American Mathematical Society . Jun2019, Vol. 147 Issue 6, p2437-2451. 15p. - Publication Year :
- 2019
-
Abstract
- This paper is devoted to exponential dichotomies of nonautonomous difference equations. Under the assumptions that (Am)m∈Z is a sequence of bounded operators acting on an arbitrary Banach space X that admits a uniform exponential dichotomy and that (Bm)m∈Z is a sequence of compact operators such that lim|m|→∞||Bm|| = 0, D. Henry proved that either the sequence (Am+Bm)m∈Z admits a uniform exponential dichotomy or there exists a bounded nonzero sequence (xm)m∈Z ⊂ X such that xm+1 = (Am +Bm)xm for each m ∈ Z. In this paper we prove Henry's result in the setting of 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 147
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 136530655
- Full Text :
- https://doi.org/10.1090/proc/14444