کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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840982 | 908497 | 2011 | 24 صفحه PDF | دانلود رایگان |
The aim of this paper is to characterise those compact subsets KK of 33-manifolds MM that are (stable and not necessarily global) attractors for some flow on MM. We will show that it is the topology of M−KM−K, rather than that of KK, the one that plays a relevant role in this problem.A necessary and sufficient condition for a set KK to be an attractor is that it must be an “almost tame” subset of MM in a sense made precise under the equivalent notions of “weakly tame” and “tamely embedded up to shape”, defined in the paper. These are complemented by a further equivalent condition, “algebraic tameness”, which has the advantage of being checkable by explicit computation.A final section of the paper is devoted to a partial analysis of the same question when one replaces flows by discrete dynamical systems.
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 74, Issue 17, December 2011, Pages 6162–6185