Hyperbolic control sets and chain control sets

被引：12

作者：

Colonius F. ^{[1
]}

Du W. ^{[2
]}

机构：

[1] Institut für Mathematik, Universität Augsburg

[2] Mathematical Department, Harbin Engineering University

来源：

关键词：

Control sets; Hyperbolicity; Shadowing lemma;

D O I：

10.1023/A:1026645605711

中图分类号：

学科分类号：

摘要：

A shadowing lemma for hyperbolic control flows is proved. A consequence is that hyperbolic chain control sets are closures of control sets.

引用

页码：49 / 59

页数：10

共 6 条

[1]

Colonius F., Kliemann W., The Morse spectrum of linear flows on vector bundles, Trans. Amer. Math. Soc., 348, pp. 4355-4388, (1996)

[2]

The Dynamics of Control, (2000)

[3]

Mergers of control sets, Proc. Conf. Math. Theory Networks and Systems, (2000)

[4]

Franke J., Selgrade J., Hyperbolicity and chain recurrence, J. Differ. Equations, 26, pp. 27-36, (1977)

[5]

Grunvogel S., Control Sets and Lyapunov Spectrum, (2000)

[6]

Meyer K.R., Sell G.R., Melnikov transforms, Bernoulli bundles and almost periodic perturbations, Trans. Amer. Math. Soc., 129, pp. 63-105, (1989)