H E Lomelí and J D Meiss 2003 Nonlinearity 16 1573 doi:10.1088/0951-7715/16/5/302
H E Lomelí and J D Meiss
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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.
37E30 Homeomorphisms and diffeomorphisms of planes and surfaces
Issue 5 (September 2003)
Received 20 November 2002, in final form 14 May 2003
Published 20 June 2003
H E Lomelí and J D Meiss 2003 Nonlinearity 16 1573
Hans Ringström 2004 Class. Quantum Grav. 21 S305
M J Rave and W C Kerr 2010 Eur. J. Phys. 31 15
E G Kalnins and W Miller Jr 1982 J. Phys. A: Math. Gen. 15 2699
W.J. Hogan et al 2001 Nucl. Fusion 41 567
F De Zela 2005 J. Opt. B: Quantum Semiclass. Opt. 7 372
A van den Bos 1977 J. Phys. E: Sci. Instrum. 10 753
S Djordjevic et al 2008 Metrologia 45 429
H Ezawa and M Leventhal 1975 J. Phys. B: At. Mol. Phys. 8 1824
1998 Phys. Educ. 33