On the local structure of Ω-limit sets of maps
On the local structure of Ω-limit sets of maps
复制标题
Ω极限映射集的局部结构
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
P. Polácik
中科院分区：
文献类型：
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作者：
P. Brunovský;P. Polácik
设X是Banach空间设F: X→X = C1， F(0) = 0。证明了在一定条件下，轨迹的ω极限集一旦包含0，就包含0的不稳定流形中一个不同于0的点。F上的条件涉及F '(0)的谱（意味着存在稳定、不稳定、中心-不稳定和0的中心流形）和F在0的中心流形上的动力学。此外，假设0的中心不稳定空间是有限维的，或者轨迹是相对紧凑的。在一些特殊情况下，这个结果可以证明轨迹的收敛性。数学学科分类（1991）。34d05 34b40 34c40。
Let X be a Banach space and let F : X → X be C1, F (0) = 0. It is proved that, under certain conditions, the ω-limit set of a trajectory contains a point of the unstable manifold of 0 different from 0 as soon as it contains 0. The conditions on F involve the spectrum of F ′(0) (implying the existence of stable, unstable, center-unstable and center manifolds of 0) and the dynamics of F on the center manifold of 0. In addition, it is assumed that either the center-unstable space of 0 is finite dimensional or the trajectory is relatively compact. In a number of particular cases this result allows to prove convergence of trajectories. Mathematics Subject Classification (1991). 34D05, 34B40, 34C40.