Chaos arising near a topologically transversal homoclinic set
Keywords
Diffeomorphisms, hyperbolic fixed points, invariant manifolds, topological transversality, chaosAbstract
A diffeomorphism on a $C^1$-smooth manifold is studied possessing a hyperbolic fixed point. If the stable and unstable manifolds of the hyperbolic fixed point have a nontrivial local topological crossing then a chaotic behaviour of the diffeomorphism is shown. A perturbed problem is also studied by showing the relationship between a corresponding Melnikov function and the nontriviality of a local topological crossing of invariant manifolds for the perturbed diffeomorphism.Downloads
Published
2002-12-01
How to Cite
1.
BATTELLI, Flaviano and FEČKAN, Michal. Chaos arising near a topologically transversal homoclinic set. Topological Methods in Nonlinear Analysis. Online. 1 December 2002. Vol. 20, no. 2, pp. 195 - 215. [Accessed 29 March 2024].
Issue
Section
Articles
Stats
Number of views and downloads: 0
Number of citations: 0