Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps

Details Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps

2002-11-18

arxiv.org/abs/nlin/0211027v1

Nonlinearity 16(5): 1573-1595 (2003)

Nonlinear Sciences

Chaotic Dynamics

LaTex with 10 eps figures

Scientific paper

10.1088/0951-7715/16/5/302

We develop a Melnikov method for volume-preserving maps 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

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