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Onset of secular chaos in planetary systems: period doubling and strange attractors

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Abstract

As a result of resonance overlap, planetary systems can exhibit chaotic motion. Planetary chaos has been studied extensively in the Hamiltonian framework, however, the presence of chaotic motion in systems where dissipative effects are important, has not been thoroughly investigated. Here, we study the onset of stochastic motion in presence of dissipation, in the context of classical perturbation theory, and show that planetary systems approach chaos via a period-doubling route as dissipation is gradually reduced. Furthermore, we demonstrate that chaotic strange attractors can exist in mildly damped systems. The results presented here are of interest for understanding the early dynamical evolution of chaotic planetary systems, as they may have transitioned to chaos from a quasi-periodic state, dominated by dissipative interactions with the birth nebula.

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Authors and Affiliations

  1. Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, 91125, USA

    Konstantin Batygin

  2. Departement Cassiopée, Universite de Nice-Sophia Antipolis, Observatoire de la Côte dAzur, CNRS 4, 06304, Nice, France

    Konstantin Batygin & Alessandro Morbidelli

Authors
  1. Konstantin Batygin
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  2. Alessandro Morbidelli
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Correspondence to Konstantin Batygin.

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Batygin, K., Morbidelli, A. Onset of secular chaos in planetary systems: period doubling and strange attractors. Celest Mech Dyn Astr 111, 219–233 (2011). https://doi.org/10.1007/s10569-011-9361-3

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  • DOI: https://doi.org/10.1007/s10569-011-9361-3

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