Chaos arising near a topologically transversal homoclinic set
Słowa kluczowe
Diffeomorphisms, hyperbolic fixed points, invariant manifolds, topological transversality, chaosAbstrakt
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.Pobrania
Opublikowane
2002-12-01
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1.
BATTELLI, Flaviano & FEČKAN, Michal. Chaos arising near a topologically transversal homoclinic set. Topological Methods in Nonlinear Analysis [online]. 1 grudzień 2002, T. 20, nr 2, s. 195–215. [udostępniono 22.7.2024].
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