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Homoclinic crossing in open systems: Chaos in periodically perturbed monopole plus quadrupolelike potentials

P. S. Letelier·A. E. Motter
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Abstract

The Melnikov method is applied to periodically perturbed open systems modeled by an inverse--square--law attraction center plus a quadrupolelike term. A compactification approach that regularizes periodic orbits at infinity is introduced. The (modified) Smale-Birkhoff homoclinic theorem is used to study transversal homoclinic intersections. A larger class of open systems with degenerated (nonhyperbolic) unstable periodic orbits after regularization is also briefly considered.

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P. S. Letelier, A. E. Motter. 2002-03-23. Homoclinic crossing in open systems: Chaos in periodically perturbed monopole plus quadrupolelike potentials. https://doi.org/10.1103/physreve.60.3920

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