Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps

Abstract

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

LaTex with 10 eps figures

Cited by in corpus (7)

• Resonance Zones and Lobe Volumes for Volume-Preserving Maps
• Nilpotent normal form for divergence-free vector fields and volume-preserving maps
• Chaotic Advection and the Emergence of Tori in the Küppers-Lortz State
• Canonical Melnikov theory for diffeomorphisms
• Numerical Computation of the Stable and Unstable Manifolds of Invariant Tori
• Power-law trapping in the volume-preserving Arnold-Beltrami-Childress map
• Topological Dynamics of Volume-Preserving Maps Without an Equatorial Heteroclinic Curve