TRANSPORT IN DYNAMICAL ASTRONOMY AND MULTIBODY PROBLEMS

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

doi:10.1142/9789812774569_0001

TRANSPORT IN DYNAMICAL ASTRONOMY AND MULTIBODY PROBLEMS

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

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

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 language	English
Title of host publication	Modeling and Computations in Dynamical Systems
Subtitle of host publication	In Commemoration of the 100th Anniversary of the Birth of John von Neumann
Publisher	World Scientific Publishing Co.
Pages	3-31
Number of pages	29
ISBN (Electronic)	9789812774569
ISBN (Print)	9812565965
DOIs	https://doi.org/10.1142/9789812774569_0001
State	Published - 1 Jan 2006
Externally published	Yes

Keywords

Three-body problem
almost invariant sets
dynamical systems
graph partitioning
invariant manifolds
lobe dynamics
set-oriented methods
transport rates

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10.1142/9789812774569_0001

Cite this

Dellnitz, M., Junge, O., Koon, W. S., Lekien, F., Lo, M. W., Marsden, J. E., Padberg, K., Preis, R., Ross, S. D., & Thiere, B. (2006). TRANSPORT IN DYNAMICAL ASTRONOMY AND MULTIBODY PROBLEMS. In Modeling and Computations in Dynamical Systems: In Commemoration of the 100th Anniversary of the Birth of John von Neumann (pp. 3-31). World Scientific Publishing Co.. https://doi.org/10.1142/9789812774569_0001

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title = "TRANSPORT IN DYNAMICAL ASTRONOMY AND MULTIBODY PROBLEMS",

abstract = "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.",

keywords = "Three-body problem, almost invariant sets, dynamical systems, graph partitioning, invariant manifolds, lobe dynamics, set-oriented methods, transport rates",

author = "Michael Dellnitz and Oliver Junge and Koon, {Wang Sang} and Francois Lekien and Lo, {Martin W.} and Marsden, {Jerrold E.} and Kathrin Padberg and Robert Preis and Ross, {Shane D.} and Bianca Thiere",

note = "Publisher Copyright: {\textcopyright} 2006 by World Scientific Publishing Co. Pte. Ltd.",

year = "2006",

month = jan,

day = "1",

doi = "10.1142/9789812774569_0001",

language = "English",

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Dellnitz, M, Junge, O, Koon, WS, Lekien, F, Lo, MW, Marsden, JE, Padberg, K, Preis, R, Ross, SD & Thiere, B 2006, TRANSPORT IN DYNAMICAL ASTRONOMY AND MULTIBODY PROBLEMS. in Modeling and Computations in Dynamical Systems: In Commemoration of the 100th Anniversary of the Birth of John von Neumann. World Scientific Publishing Co., pp. 3-31. https://doi.org/10.1142/9789812774569_0001

TRANSPORT IN DYNAMICAL ASTRONOMY AND MULTIBODY PROBLEMS. / Dellnitz, Michael; Junge, Oliver; Koon, Wang Sang et al.
Modeling and Computations in Dynamical Systems: In Commemoration of the 100th Anniversary of the Birth of John von Neumann. World Scientific Publishing Co., 2006. p. 3-31.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - TRANSPORT IN DYNAMICAL ASTRONOMY AND MULTIBODY PROBLEMS

AU - Dellnitz, Michael

AU - Junge, Oliver

AU - Koon, Wang Sang

AU - Lekien, Francois

AU - Lo, Martin W.

AU - Marsden, Jerrold E.

AU - Padberg, Kathrin

AU - Preis, Robert

AU - Ross, Shane D.

AU - Thiere, Bianca

PY - 2006/1/1

Y1 - 2006/1/1

N2 - 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.

AB - 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.

KW - Three-body problem

KW - almost invariant sets

KW - dynamical systems

KW - graph partitioning

KW - invariant manifolds

KW - lobe dynamics

KW - set-oriented methods

KW - transport rates

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DO - 10.1142/9789812774569_0001

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SN - 9812565965

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EP - 31

BT - Modeling and Computations in Dynamical Systems

PB - World Scientific Publishing Co.

ER -

TRANSPORT IN DYNAMICAL ASTRONOMY AND MULTIBODY PROBLEMS

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