Chaos arising near a topologically transversal homoclinic set

Flaviano Battelli, Michal Fečkan

DOI: http://dx.doi.org/10.12775/TMNA.2002.033

Abstract


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.

Keywords


Diffeomorphisms; hyperbolic fixed points; invariant manifolds; topological transversality; chaos

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