Liapunov stability and adding machines
Liapunov stability and adding machines
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DOI：
10.1017/s0143385700008373
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发表时间：
1995-04
影响因子：
0.9
通讯作者：
J. Buescu;I. Stewart
中科院分区：
文献类型：
--
作者：
J. Buescu;I. Stewart
设X是局部连通局部紧度量空间，f：X → X是连续映射。设A是f下的紧传递集。如果A是渐近稳定的，则它有200个连通分支，这些连通分支是循环置换的。如果它是李雅普诺夫稳定的，那么A可以有无穷多个连通分支。我们的主要结果指出，这些形成一个康托集上的f是拓扑共轭的加法机。一些后果的推导，包括一个完整的分类的紧凑的连续映射的区间和Liapunov不稳定性的不变康托集Denjoy映射的圆的连续映射集。
Abstract Let X be a locally connected locally compact metric space and f: X → X a continuous map. Let A be a compact transitive set under f. If A is asymptotically stable, then it has finitely many connected components, which are cyclically permuted. If it is Liapunov stable, then A may have infinitely many connected components. Our main result states that these form a Cantor set on which f is topologically conjugate to an adding machine. A number of consequences are derived, including a complete classification of compact transitive sets for continuous maps of the interval and the Liapunov instability of the invariant Cantor set of Denjoy maps of the circle.