Connected components of attractors and other stable sets
Connected components of attractors and other stable sets
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吸引子和其他稳定集的连通分量
DOI：
10.1007/bf02215978
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
M. Hurley
中科院分区：
文献类型：
--
作者：
M. Hirsch;M. Hurley
研究了连续映射在局部连通度量空间上的作用，重点研究了连续映射在吸引子连通分支空间上的作用，得到了吸引子的主要结果是：如果A是C.Conley意义下的吸引子，则A的分支置换，且置换是循环的当且仅当吸引子不可分解.这与Buescu和Stewart最近获得的类似结果有关。在不可分解稳定不变集的情况下，我们证明了无论是Y的分量对吸引子的作用如上所述，或者Y有无穷多个分量，它们对它们的作用是广义加法机，因此Y中不存在周期点。
We study the action of a continuous mapfon a locally connected metric space, with an emphasis on the action induced byfon the space of connected components of an attractorAor a stable setYoff.The main result for attractors is that, ifAis an attractor in the sense of C. Conley, thenfpermutes the components ofAand that the permutation is cyclic if and only if the attractor is indecomposable. This is related to similar results obtained recently by Buescu and Stewart. In the case of an indecomposable stable invariant setYwe show that either the action offon the components ofYis as described above for the action on the attractor, or elseYhas infinitely many components, the action offon them is a generalized adding machine, so that there are no periodic points inY.Results along these lines are due to Buescu and Stewart and to Melbourne, Dellnitz and Golubitsky.