標題: | Covering relations and Lyapunov condition for topological conjugacy |
作者: | Li, Ming-Chia Lyu, Ming-Jiea 應用數學系 Department of Applied Mathematics |
關鍵字: | non-autonomous systems;topological conjugacy;covering relations;Lyapunov condition;stability |
公開日期: | 2-一月-2016 |
摘要: | In this paper, we study stability of non-autonomous discrete dynamical systems. For a two-sided non-autonomous systems with covering relations determined by a transition matrix A, we show that any small C-0 perturbed system has a sequence of compact invariant sets restricted to which the system is topologically semi-conjugate to sigma(A), the two-sided subshift of finite type induced by A. Together with Lyapunov condition of good rate, the semi-conjugacy will become conjugacy. Moreover, if the Lyapunov condition is strict and has perfect rate, then any small C-1 perturbed systems is topological conjugate to sigma(A). We also study topological chaos of one-sided systems and systems with limit functions. Lack of hyperbolicity and the time dependence of the rate prevent us from applying classical hyperbolic results or earlier works for autonomous systems: cone condition and Lyapunov function. Two examples are provided to demonstrate the existence of a non-trivial, non-hyperbolic invariant and essential of controlling rate. |
URI: | http://dx.doi.org/10.1080/14689367.2015.1020286 http://hdl.handle.net/11536/129498 |
ISSN: | 1468-9367 |
DOI: | 10.1080/14689367.2015.1020286 |
期刊: | DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL |
Volume: | 31 |
起始頁: | 60 |
結束頁: | 78 |
顯示於類別: | 期刊論文 |