Transport in dynamical astronomy and multibody problems

Research output: Journal contributionsJournal articlesResearchpeer-review


  • Michael Dellnitz
  • Oliver Junge
  • Wang Sang Koon
  • Francois Lekien
  • Martin W. Lo
  • Jerrold E. Marsden
  • Kathrin Padberg
  • Robert Preis
  • Shane D. Ross
  • Bianca Thiere

We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new computational technique for computing key dynamical features, including almost invariant sets, resonance regions as well as transport rates and bottlenecks between regions in dynamical systems. This methodology can be applied to a variety of multibody problems, including those in molecular modeling, chemical reaction rates and dynamical astronomy. In this paper we focus on problems in dynamical astronomy to illustrate the power of the combination of these different numerical tools and their applicability. In particular, we compute transport rates between two resonance regions for the three-body system consisting of the Sun, Jupiter and a third body (such as an asteroid). These resonance regions are appropriate for certain comets and asteroids.

Original languageEnglish
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number3
Pages (from-to)699-727
Number of pages29
Publication statusPublished - 03.2005
Externally publishedYes

Bibliographical note

Funding Information:
This research was partly supported by the DAAD, DFG Priority Program 1095, NSF-ITR grant ACI-0204932, a Max Planck Research Award and the California Institute of Technology President’s Fund. This work was carried out in part at the Jet Propulsion Laboratory and California Institute of Technology under a contract with National Aeronautics and Space Administration.

    Research areas

  • Almost invariant sets, Dynamical systems, Graph partitioning, Invariant manifolds, Lobe dynamics, Set-oriented methods, Three-body problem, Transport rates
  • Mathematics