Abstract. 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.

Mathematics Subject Classification: 34C20, 34C35, 34C37, 58F05, 70H99

Print publication: Issue 5 (September 2003)
Received 20 November 2002, in final form 14 May 2003
Published 20 June 2003