The validity of Sundman-type asymptotic estimates for collision solutions is established for a wide class of dynamical systems with singular forces, including the classical n-body problems with Newtonian, quasi-homogeneous and logarithmic potentials. The solutions are meant in the generalized sense of Morse (locally-in space and time-minimal trajectories with respect to compactly supported variations) and their uniform limits. The analysis includes the extension of the Von Zeipel's theorem and the proof of isolatedness of collisions. Furthermore, such asymptotic analysis is applied to prove the absence of collisions for locally minimal trajectories. © The Author 2008. Published by Oxford University Press. All rights reserved.

Barutello, V., Ferrario, D., Terracini, S. (2008). On the singularities of generalized solutions to $n$-body-type problems. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2008(Article ID rnn069), 1-78 [10.1093/imrn/rnn069].

On the singularities of generalized solutions to $n$-body-type problems

FERRARIO, DAVIDE LUIGI;TERRACINI, SUSANNA
2008

Abstract

The validity of Sundman-type asymptotic estimates for collision solutions is established for a wide class of dynamical systems with singular forces, including the classical n-body problems with Newtonian, quasi-homogeneous and logarithmic potentials. The solutions are meant in the generalized sense of Morse (locally-in space and time-minimal trajectories with respect to compactly supported variations) and their uniform limits. The analysis includes the extension of the Von Zeipel's theorem and the proof of isolatedness of collisions. Furthermore, such asymptotic analysis is applied to prove the absence of collisions for locally minimal trajectories. © The Author 2008. Published by Oxford University Press. All rights reserved.
Articolo in rivista - Articolo scientifico
N-body problem, singularities, collisions
English
2008
2008
Article ID rnn069
1
78
none
Barutello, V., Ferrario, D., Terracini, S. (2008). On the singularities of generalized solutions to $n$-body-type problems. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2008(Article ID rnn069), 1-78 [10.1093/imrn/rnn069].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/5326
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