Please use this identifier to cite or link to this item:
Title: Whiskered Parabolic Tori in the Planar (n+1)-Body Problem
Author: Baldomá, Inmaculada
Fontich, Ernest, 1955-
Martín, Pau
Keywords: Sistemes hamiltonians
Sistemes dinàmics diferenciables
Hamiltonian systems
Differentiable dynamical systems
Issue Date: 12-Jul-2019
Publisher: Springer Verlag
Abstract: Abstract: The planar $(n+1)$-body problem models the motion of $n+1$ bodies in the plane under their mutual Newtonian gravitational attraction forces. When $n \geq 3$, the question about final motions, that is, what are the possible limit motions in the planar $(n+1)$-body problem when $t \rightarrow \infty$, ceases to be completely meaningful due to the existence of non-collision singularities. In this paper we prove the existence of solutions of the planar $(n+1)$-body problem which are defined for all forward time and tend to a parabolic motion, that is, that one of the bodies reaches infinity with zero velocity while the rest perform a bounded motion. These solutions are related to whiskered parabolic tori at infinity, that is, parabolic tori with stable and unstable invariant manifolds which lie at infinity. These parabolic tori appear in cylinders which can be considered 'normally parabolic'. The existence of these whiskered parabolic tori is a consequence of a general theorem on parabolic tori developed in this paper. Another application of our theorem is a conjugation result for a class of skew product maps with a parabolic torus with its normal form generalizing results of Takens (Ann Inst Fourier 23(2):163-195, 1973), and Voronin (Funktsional Anal i Prilozhen 15(1):1-17, 96, 1981).
Note: Versió postprint del document publicat a:
It is part of: Communications in Mathematical Physics, 2019, vol. 374, p. 63-110
Related resource:
ISSN: 0010-3616
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

Files in This Item:
File Description SizeFormat 
709599.pdf626.56 kBAdobe PDFView/Open

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.