Abstract
We study the dynamics near the intersection of a weaker and a stronger resonance inn-degree-of-freedom, nearly integrable Hamiltonian systems. For a truncated normal form we show the existence of (n−2)-dimensional hyperbolic invariant tori whose whiskers intersect inmultipulse homoclinic orbits with large splitting angles. The homoclinic obits are doubly asymptotic to solutions that “diffuse” across the weak resonance along the strong resonance. We derive a universalhomoclinic tree that describes the bifurcations of these orbits, which are shown to survive in the full normal form. We illustrate our results on a three-degree-of-freedom mechanical system.
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Haller, G. Universal homoclinic bifurcations and chaos near double resonances. J Stat Phys 86, 1011–1051 (1997). https://doi.org/10.1007/BF02183612
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DOI: https://doi.org/10.1007/BF02183612