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Heteroclinic intersections between invariant circles of volume-preserving maps

H E Lomelí and J D Meiss

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Recommended by K Ohkitani

We develop a Melnikov method for volume-preserving maps that have normally hyperbolic invariant sets with codimension-one invariant manifolds. The Melnikov function is shown to be related to the flux of the perturbation through the unperturbed invariant surface. As an example, we compute the Melnikov function for a perturbation of a three-dimensional map that has a heteroclinic connection between a pair of invariant circles. The intersection curves of the manifolds are shown to undergo bifurcations in homology.


PACS

02.40.Sf Manifolds and cell complexes

05.45.Ra Coupled map lattices

MSC

37E30 Homeomorphisms and diffeomorphisms of planes and surfaces

58C25 Differentiable maps

37C29 Homoclinic and heteroclinic orbits

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 5 (September 2003)

Received 20 November 2002, in final form 14 May 2003

Published 20 June 2003



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