標題: TOPOLOGICAL CONJUGACY FOR LIPSCHITZ PERTURBATIONS OF NON-AUTONOMOUS SYSTEMS
作者: Li, Ming-Chia
Lyu, Ming-Jiea
應用數學系
Department of Applied Mathematics
關鍵字: Topological conjugacy;exponential dichotomy;Lipschitz perturbation;non-autonomous systems;nonuniformly hyperbolic systems
公開日期: Sep-2016
摘要: In this paper, topological conjugacy for two-sided non-hyperbolic and non-autonomous discrete dynamical systems is studied. It is shown that if the system has covering relations with weak Lyapunov condition determined by a transition matrix, there exists a sequence of compact invariant sets restricted to which the system is topologically conjugate to the two-sided subshift of finite type induced by the transition matrix. Moreover, if the systems have covering relations with exponential dichotomy and small Lipschitz perturbations, then there is a constructive verification proof of the weak Lyapunov condition, and so topological dynamics of these systems are fully understood by symbolic representations. In addition, the tolerance of Lipschitz perturbation can be characterised by the dichotomy tuple. Here, the weak Lyapunov condition is adapted from [12, 21, 15] and the exponential dichotomy is from [2].
URI: http://dx.doi.org/10.3034/dcds.2016017
http://hdl.handle.net/11536/133865
ISSN: 1078-0947
DOI: 10.3034/dcds.2016017
期刊: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume: 36
Issue: 9
起始頁: 5011
結束頁: 5024
Appears in Collections:Articles