Lyapunov stability of $\omega$-limit sets

Carlos Arnoldo Morales; M. J. Pacifico

doi:10.3934/dcds.2002.8.671

Article Contents

2002, Volume 8, Issue 3: 671-674. Doi: 10.3934/dcds.2002.8.671

This issue Previous Article Lipschitz continuous solutions of some doubly nonlinear parabolic equations Next Article Existence and uniform decay for the Euler-Bernoulli viscoelastic equation with nonlocal boundary dissipation

Lyapunov stability of $\omega$-limit sets

Carlos Arnoldo Morales^1, and
M. J. Pacifico^2,

1.
Instituto de Matemàtica, Universidade Federal do Rio de Janeiro, C. P. 68530, CEP 21945-970, Rio de Janeiro
2.
Instituto de Matemàtica, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro

Received: March 31, 2001

Revised: June 30, 2001

Published: June 2002

Abstract Related Papers Cited by

Abstract

We prove that there is a residual subset $C$, in the space of all $\mathcal C^1$ vector fields of a closed $n$-manifold $M$, such that for every $X \in \mathcal R$ the set of points in $M$ with Lyapunov stable $\omega$-limit set is residual in $M$. This improves a result in Arnaud [1] and gives a partial solution to a conjecture in Hurley [8].

Keywords:

Mathematics Subject Classification: Primary: 37Dxx, 37Bxx, 34Bxx.

Citation:

Article Metrics

HTML views() PDF downloads(182) Cited by(0)

Lyapunov stability of $\omega$-limit sets

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Lyapunov stability of $\omega$-limit sets

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content