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arXiv · 0812.1810

Resonance Zones and Lobe Volumes for Volume-Preserving Maps

H. E. Lomelí·J. D. Meiss
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Abstract

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.

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H. E. Lomelí, J. D. Meiss. 2008-12-09. Resonance Zones and Lobe Volumes for Volume-Preserving Maps. https://doi.org/10.1088/0951-7715%2F22%2F8%2F001

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