Periodic linear motions with multiple collisions in a forced Kepler type problem
type: Item
instance of: scholarly article
title: Periodic linear motions with multiple collisions in a forced Kepler type problem
zbMATH Open document ID: 1441.70006
author: Carlota Rebelo
author: Alexandre Simões
published in: Discrete and Continuous Dynamical Systems
publication date: 2018-08-16T00:00:00Z
review text: In this paper the authors extend the proof of the existence of multiple periodic linear motions with collisions for a periodically forced Kepler problem, presented by R. Ortega [Port. Math. (N.S.) 68, No. 2, 149--176 (2011; Zbl 1235.34136)] , in the equation $\ddot{u} =-1/u^2+p(t)\), \(u>0\), to a forced Kepler type problem \(\ddot{u} =-1/u^\alpha+p(t)\), \(u>0\), \(\alpha=2\) or \(\alpha\ge 4\). They generalize the results of Ortega for the existence of positive periodic solutions with \(n\) collisions in the interval \([0,2M\pi]\), for each \(M\) and \(n\). For this proof, the authors apply the Poincaré-Birkhoff theorem. The paper ends with no conclusions but there is an Appendix, where the authors present some auxiliary proofs.
reviewed by: Maria Gousidou-Koutita
Mathematics Subject Classification ID: 70F17
Mathematics Subject Classification ID: 70K40
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37E40
zbMATH DE Number: 6919404
zbMATH Keywords: multiple collisions
zbMATH Keywords: periodic solution
zbMATH Keywords: Poincaré-Birkhoff theorem
MaRDI profile type: Publication
full work available at URL: dcds.2018172
OpenAlex ID: W2805457334
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Wikidata QID: Q129696879
DOI: 10.3934/DCDS.2018172
description: scientific article; zbMATH DE number 6919404