Local expansion concepts for detecting transport barriers in dynamical systems
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In: Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 12, 12.2009, p. 4176-4190.
Research output: Journal contributions › Journal articles › Research › peer-review
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TY - JOUR
T1 - Local expansion concepts for detecting transport barriers in dynamical systems
AU - Padberg, Kathrin
AU - Thiere, Bianca
AU - Preis, Robert
AU - Dellnitz, Michael
PY - 2009/12
Y1 - 2009/12
N2 - 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.
AB - 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.
KW - Almost invariant sets
KW - Dynamical systems
KW - Expansion
KW - Graph theory
KW - Invariant manifolds
KW - Set-oriented methods
KW - Transport barriers
KW - Didactics of Mathematics
UR - http://www.scopus.com/inward/record.url?scp=67349158008&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/40b58354-f5b2-3235-b7b8-c2dcffbeb3bd/
U2 - 10.1016/j.cnsns.2009.03.018
DO - 10.1016/j.cnsns.2009.03.018
M3 - Journal articles
AN - SCOPUS:67349158008
VL - 14
SP - 4176
EP - 4190
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
IS - 12
ER -