Non-existence of wandering intervals and structure of topological attractors of one dimensional dynamical systems: 1. The case of negative Schwarzian derivative
Non-existence of wandering intervals and structure of topological attractors of one dimensional dynamical systems: 1. The case of negative Schwarzian derivative
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DOI：
10.1017/s0143385700005307
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发表时间：
1989-12
影响因子：
0.9
通讯作者：
M. Lyubich
中科院分区：
文献类型：
--
作者：
M. Lyubich
摘要证明了任意具有负Schwarzian导数和非退化临界点的一维动力系统不存在游荡区间。这一结果意味着这样一个系统的动力学的一个相当完整的视图。特别地，每一个极小拓扑吸引子要么是极限环，要么是带边界的一维流形，要么是螺线管。一般点的轨道趋向于某个极小吸引子。
Abstract It is proved that an arbitrary one dimensional dynamical system with negative Schwarzian derivative and non-degenerate critical points has no wandering intervals. This result implies a rather complete view of the dynamics of such a system. In particular, every minimal topological attractor is either a limit cycle, or a one dimensional manifold with boundary, or a solenoid. The orbit of a generic point tends to some minimal attractor.