Local expansion concepts for detecting transport barriers in dynamical systems

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Authors

In the last two decades, the mathematical analysis of material transport has received considerable interest in many scientific fields such as ocean dynamics and astrodynamics. In this contribution we focus on the numerical detection and approximation of transport barriers in dynamical systems. Starting from a set-oriented approximation of the dynamics we combine discrete concepts from graph theory with established geometric ideas from dynamical systems theory. We derive the global transport barriers by computing the local expansion properties of the system. For the demonstration of our results we consider two different systems. First we explore a simple flow map inspired by the dynamics of the global ocean. The second example is the planar circular restricted three body problem with Sun and Jupiter as primaries, which allows us to analyze particle transport in the solar system.

Original languageEnglish
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume14
Issue number12
Pages (from-to)4176-4190
Number of pages15
ISSN1007-5704
DOIs
Publication statusPublished - 12.2009
Externally publishedYes

    Research areas

  • Almost invariant sets, Dynamical systems, Expansion, Graph theory, Invariant manifolds, Set-oriented methods, Transport barriers
  • Didactics of Mathematics

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