Equivalences between nonuniform exponential dichotomy and admissibility

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Zhou, Linfeng¹  Lu, Kening²  Zhang, Weinian¹ 

[1] Sichuan Univ, Sch Math, Chengdu 610064, Sichuan, Peoples R China

[2] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

关键词: Nonuniformity;    Exponential dichotomy;    Bounded growth;    Admissibility;    Continuous norms;   

DOI  :  10.1016/j.jde.2016.09.035

来源: Elsevier

【 摘 要 】

Relationship between exponential dichotomies and admissibility of function classes is a significant problem for hyperbolic dynamical systems. It was proved that a nonuniform exponential dichotomy implies several admissible pairs of function classes and conversely some admissible pairs were found to imply a nonuniform exponential dichotomy. In this paper we find an appropriate admissible pair of classes of Lyapunov bounded functions which is equivalent to the existence of nonuniform exponential dichotomy on half-lines R-+/- separately, on both half-lines R-+/- simultaneously, and on the whole line R. Additionally, the maximal admissibility is proved in the case on both half-lines RI simultaneously. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free