A Mel'nikov vector for N-dimensional mappings

T. Bountis, A. Goriely, M. Kollmann

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


We use the Fredholm alternative to derive a Mel'nikov vector for perturbations of N-dimensional maps with homoclinic connections. If the unperturbed mapping is integrable, this vector assumes a simple form, which we use to determine conditions for transversal and tangential intersection between the invariant manifolds in a four-dimensional map of the McMillan type. We also discuss conditions for non-transversal intersection which accurately predict the crossing of invariant manifolds from one part of 4-D space into another.

Original languageEnglish
Pages (from-to)38-48
Number of pages11
JournalPhysics Letters A
Issue number1-2
Publication statusPublished - Oct 2 1995

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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