Topological dynamics for multidimensional perturbations of maps with covering relations and Liapunov condition

Ming-Chia Li*, Ming Jiea Lyu

*Corresponding author for this work

研究成果: Article

5 引文 斯高帕斯(Scopus)

摘要

In this paper, we study topological dynamics of high-dimensional systems which are perturbed from a continuous map on Rm×Rk of the form (f(x),g(x,y)). Assume that f has covering relations determined by a transition matrix A. If g is locally trapping, we show that any small C0 perturbed system has a compact positively invariant set restricted to which the system is topologically semi-conjugate to the one-sided subshift of finite type induced by A. In addition, if the covering relations satisfy a strong Liapunov condition and g is a contraction, we show that any small C1 perturbed homeomorphism has a compact invariant set restricted to which the system is topologically conjugate to the two-sided subshift of finite type induced by A. Some other results about multidimensional perturbations of f are also obtained. The strong Liapunov condition for covering relations is adapted with modification from the cone condition in Zgliczyński (2009) [11]. Our results extend those in Juang et al. (2008) [1], Li et al. (2008) [2], Li and Malkin (2006) [3], Misiurewicz and Zgliczyński (2001) [4] by considering a larger class of maps f and their multidimensional perturbations, and by concluding conjugacy rather than entropy. Our results are applicable to both the logistic and Hénon families.

原文English
頁(從 - 到)799-812
頁數14
期刊Journal of Differential Equations
250
發行號2
DOIs
出版狀態Published - 15 一月 2011

指紋 深入研究「Topological dynamics for multidimensional perturbations of maps with covering relations and Liapunov condition」主題。共同形成了獨特的指紋。

  • 引用此