TY - JOUR

T1 - A Mel'nikov vector for N-dimensional mappings

AU - Bountis, T.

AU - Goriely, A.

AU - Kollmann, M.

N1 - Funding Information:
We are indebtedt o the refereesf or their critical commentsa nd useful remarks.W e also thank M.N. Vrahatis and V.M. Rothos for interestingd iscussions. Partial supportf or this work was provided by the “Human Capital and Mobility” EEC contracts No. CHRX-CT93-0107, No. CHRX-CT94-0980 as well as a P.EN.E.D. grant from the Secretariato f Energy and Technology of the Greek Ministry of Industry, Energy and Technology.

PY - 1995/10/2

Y1 - 1995/10/2

N2 - 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.

AB - 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.

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U2 - 10.1016/0375-9601(95)00587-S

DO - 10.1016/0375-9601(95)00587-S

M3 - Article

AN - SCOPUS:0008142432

VL - 206

SP - 38

EP - 48

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 1-2

ER -