Local expansion concepts for detecting transport barriers in dynamical systems

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Local expansion concepts for detecting transport barriers in dynamical systems. / Padberg, Kathrin; Thiere, Bianca; Preis, Robert et al.
in: Communications in Nonlinear Science and Numerical Simulation, Jahrgang 14, Nr. 12, 12.2009, S. 4176-4190.

Publikation: Beiträge in ZeitschriftenZeitschriftenaufsätzeForschungbegutachtet

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@article{c85893339633499cb9a18f89221a0de4,
title = "Local expansion concepts for detecting transport barriers in dynamical systems",
abstract = "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.",
keywords = "Almost invariant sets, Dynamical systems, Expansion, Graph theory, Invariant manifolds, Set-oriented methods, Transport barriers, Didactics of Mathematics",
author = "Kathrin Padberg and Bianca Thiere and Robert Preis and Michael Dellnitz",
year = "2009",
month = dec,
doi = "10.1016/j.cnsns.2009.03.018",
language = "English",
volume = "14",
pages = "4176--4190",
journal = "Communications in Nonlinear Science and Numerical Simulation",
issn = "1007-5704",
publisher = "Elsevier B.V.",
number = "12",

}

RIS

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 -

DOI