Periodic linear motions with multiple collisions in a forced Kepler type problem

Carlota Rebelo; Alexandre Simões

doi:10.3934/dcds.2018172

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2018, Volume 38, Issue 8: 3955-3975. Doi: 10.3934/dcds.2018172

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Periodic linear motions with multiple collisions in a forced Kepler type problem

Carlota Rebelo^1, , and
Alexandre Simões^2,

1.
Fac. Ciências da Univ. Lisboa e Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Campo Grande, Edifício C6, piso 2, P-1749-016 Lisboa, Portugal
2.
Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Campo Grande, Edifício C6, piso 2, P-1749-016 Lisboa, Portugal

* Corresponding author: Carlota Rebelo
* Corresponding author: Carlota Rebelo

Received: September 30, 2017

Revised: February 28, 2018

Published: May 2018

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Abstract

In [7] the author proved the existence of multiple periodic linear motions with collisions for a periodically forced Kepler problem. We extend this result obtaining periodic solutions with multiple collisions for a forced Kepler type problem. In order to do that we apply the Poincaré-Birkhoff theorem.

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Mathematics Subject Classification: Primary: 34C25; Secondary: 37E40, 70K40.

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Figure 1. The restriction of a possible (according to Proposition 2) set $D$ to the strip $0\le t_0\le 2\pi$

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Figure 2. Cylinder $B$

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References

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