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When is high-dimensional scattering chaos essentially two dimensional? Measuring the product structure of singularities

G. Drótos1, C. Jung2, and T. Tél1,3

  • 1Institute of Theoretical Physics, Eötvös University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
  • 2Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Avenida Universidad sin número, Apartado Postal 48-3 Cuernavaca, Morelos, Mexico
  • 3Research Group in Theoretical Physics of the Hungarian Academy of Sciences at Eötvös University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary

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Phys. Rev. E 86, 056210 – Published 16 November, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.056210

Abstract

We demonstrate how the area of the enveloping surface of the scattering singularities in a three-degrees-of-freedom (3-dof) system depends on a perturbation parameter controlling the distance from a reducible case. This dependence is monotonic and approximately linear. Therefore it serves as a measure for this distance, which can be extracted from an investigation of the fractal structure. These features are a consequence of the dynamics being governed by normally hyperbolic invariant manifolds. We conclude that typical n-dof chaotic scattering exhibits either structures developing out of a stack of chaotic structures of 2-dof type or hardly any chaotic effects.

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Phys. Rev. E 86, 056210– Published 16 November, 2012
  • Received 9 July 2012

©2012 American Physical Society

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