• how strange can an attractor for a dynamical system in a 3-manifold look?

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    • تاریخ ارائه: 1390/01/01
    • تاریخ انتشار در تی پی بین: 1390/01/01
    • تعداد بازدید: 483
    • تعداد پرسش و پاسخ ها: 0
    • شماره تماس دبیرخانه رویداد: -
    the aim of this paper is to characterise those compact subsets k of 3-manifolds m that are (stable and not necessarily global) attractors for some flow on m. we will show that it is the topology of m−k, rather than that of k, the one that plays a relevant role in this problem. a necessary and sufficient condition for a set k to be an attractor is that it must be an “almost tame” subset of m 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.

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