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Global time-regularization of the gravitational N -body problem

M Antoñana 1 Philippe Chartier 2, 3 J Makazaga 1 A Murua 1
3 MINGUS - Multi-scale numerical geometric schemes
IRMAR - Institut de Recherche Mathématique de Rennes, ENS Rennes - École normale supérieure - Rennes, Inria Rennes – Bretagne Atlantique
Abstract : This work considers the gravitational N-body problem and introduces time-reparametrization functions that allow to define globally solutions of the N-body equations. First, a lower bound of the radius of convergence of the solution to the original equations is derived, which suggests an appropriate time-reparametrization. In the new fictitious time τ , it is then proved that any solution exists for all τ ∈ R, and that it is uniquely extended as a holomorphic function to a strip of fixed width. As a by-product, a global power series representation of the solutions of the N-body problem is obtained. Noteworthy, our global time-regularization remain valid in the limit when one of the masses vanishes. Finally, numerical experiments show the efficiency of the new time-regularization functions for some N-problems with close encounters.
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https://hal.inria.fr/hal-02431607
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Submitted on : Wednesday, January 8, 2020 - 7:45:39 AM
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  • HAL Id : hal-02431607, version 1

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M Antoñana, Philippe Chartier, J Makazaga, A Murua. Global time-regularization of the gravitational N -body problem. 2020. ⟨hal-02431607⟩

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