COVERING RELATIONS AND THE EXISTENCE OF TOPOLOGICALLY NORMALLY HYPERBOLIC INVARIANT SETS

被引：20
作者：
Capinski, Maciej J. [1 ]
机构：
[1] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2009年 / 23卷 / 03期
关键词：
Normally hyperbolic sets; covering relations; Brouwer degree; COMPUTER-ASSISTED PROOF; QUASI-PERIODIC MAPS; PARAMETERIZATION METHOD; MANIFOLDS; COMPUTATION; EQUATIONS; WHISKERS; CHAOS; TORI; SYSTEMS;
D O I：
10.3934/dcds.2009.23.705
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a topological method for the detection of normally hyperbolic type invariant sets for maps. The invariant set covers a sub-manifold without a boundary in R-k. For the method to hold we only need to assume that the movement of the system transversal to the manifold has directions of topological expansion and contraction. The movement in the direction of the manifold can be arbitrary. The result is based on the method of covering relations and local Brouwer degree theory.
引用
收藏
页码：705 / 725
页数：21
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