具有吸引子混合盆(其中一个是开的)的流形的保边映射

Q2 Mathematics

Transactions of the Moscow Mathematical Society Pub Date : 2014-11-06 DOI:10.1090/S0077-1554-2014-00241-7

Trudy Moskov, N. Solodovnikov

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引用次数: 0

摘要

．我们构造了一个c2 -微分同态的开集，它保留了流形的边界，并具有以下性质:对于每一个映射，吸引子的一个分量的吸引盆是开的且处处密集的，而第二个分量的吸引盆虽然其测度是正的，但无处密集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Boundary-preserving mappings of a manifold with intermingling basins of components of the attractor, one of which is open

. We construct an open set of C 2 -diﬀeomorphisms which preserve the boundary of some manifold, and which have the following property: for each mapping, the basin of attraction of one component of the attractor is open and everywhere dense, but the basin of attraction of the second component is nowhere dense, though its measure is positive.

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Transactions of the Moscow Mathematical Society Mathematics-Mathematics (miscellaneous)

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期刊介绍： This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.