Transport in Dynamical Astronomy and Multibody Problems

M. Dellnitz, O. Junge, W.S. Koon, F. Lekien, M.W. Lo, J.E. Marsden, K. Padberg, R. Preis, S.D. Ross, B. Thiere, International Journal of Bifurcation and Chaos (2005) 699–727.

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Journal Article | Published | English
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<jats:p> 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. </jats:p>
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International Journal of Bifurcation and Chaos
Page
699-727
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Dellnitz M, Junge O, Koon WS, et al. Transport in Dynamical Astronomy and Multibody Problems. International Journal of Bifurcation and Chaos. 2005:699-727. doi:10.1142/s0218127405012545
Dellnitz, M., Junge, O., Koon, W. S., Lekien, F., Lo, M. W., Marsden, J. E., … Thiere, B. (2005). Transport in Dynamical Astronomy and Multibody Problems. International Journal of Bifurcation and Chaos, 699–727. https://doi.org/10.1142/s0218127405012545
@article{Dellnitz_Junge_Koon_Lekien_Lo_Marsden_Padberg_Preis_Ross_Thiere_2005, title={Transport in Dynamical Astronomy and Multibody Problems}, DOI={10.1142/s0218127405012545}, journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael and Junge, Oliver and Koon, Wang Sang and Lekien, Francois and Lo, Martin W. and Marsden, Jerrold E. and Padberg, Kathrin and Preis, Robert and Ross, Shane D. and Thiere, Bianca}, year={2005}, pages={699–727} }
Dellnitz, Michael, Oliver Junge, Wang Sang Koon, Francois Lekien, Martin W. Lo, Jerrold E. Marsden, Kathrin Padberg, Robert Preis, Shane D. Ross, and Bianca Thiere. “Transport in Dynamical Astronomy and Multibody Problems.” International Journal of Bifurcation and Chaos, 2005, 699–727. https://doi.org/10.1142/s0218127405012545.
M. Dellnitz et al., “Transport in Dynamical Astronomy and Multibody Problems,” International Journal of Bifurcation and Chaos, pp. 699–727, 2005.
Dellnitz, Michael, et al. “Transport in Dynamical Astronomy and Multibody Problems.” International Journal of Bifurcation and Chaos, 2005, pp. 699–727, doi:10.1142/s0218127405012545.

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