Resonance Zones and Lobe Volumes for Volume-Preserving Maps

Details Resonance Zones and Lobe Volumes for Volume-Preserving Maps Resonance Zones and Lobe Volumes for Volume-Preserving Maps

2008-12-09

arxiv.org/abs/0812.1810v1

Nonlinearity 22: 1761-1789 (2009)

Nonlinear Sciences

Chaotic Dynamics

ams laTeX, 8 figures

Scientific paper

10.1088/0951-7715/22/8/001

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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