H E Lomelí and J D Meiss 2009 Nonlinearity 22 1761 doi:10.1088/0951-7715/22/8/001
H E Lomelí1 and J D Meiss2
Show affiliationsRecommended by D V Treschev
We study exact, volume-preserving diffeomorphisms that have heteroclinic connections between a pair of normally hyperbolic invariant manifolds. We develop a general theory of lobes, showing that the lobe volume is given by an integral of a generating form over the primary intersection, a subset of the heteroclinic orbits. Our definition reproduces the classical action formula in the planar, twist map case. For perturbations from a heteroclinic connection, the lobe volume is shown to reduce, to lowest order, to a suitable integral of a Melnikov function.
02.20.Sv Lie algebras of Lie groups
02.40.Ky Riemannian geometries
57S05 Topological properties of groups of homeomorphisms or diffeomorphisms
57S15 Compact Lie groups of differentiable transformations
57N16 Geometric structures on manifolds (See also 57M50)
Issue 8 (August 2009)
Received 9 December 2008, in final form 27 April 2009
Published 12 June 2009
H E Lomelí and J D Meiss 2009 Nonlinearity 22 1761
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