Periodic, subharmonic, and quasi-periodic oscillations under the action of a central force

Alessandro Fonda; Antonio J. Ureña

doi:10.3934/dcds.2011.29.169

Article Contents

2011, Volume 29, Issue 1: 169-192. Doi: 10.3934/dcds.2011.29.169

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Periodic, subharmonic, and quasi-periodic oscillations under the action of a central force

Alessandro Fonda^1, and
Antonio J. Ureña^2,

1.
Dipartimento di Matematica e Geoscienze, Università di Trieste, P. le Europa 1, I-34127 Trieste
2.
Departamento de Matematica Aplicada, Facultad de Ciencias, Universidad de Granada, E-18071, Granada

Received: October 31, 2009

Revised: January 31, 2010

Published: December 2010

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Abstract

We consider planar systems driven by a central force which depends periodically on time. If the force is sublinear and attractive, then there is a connected set of subharmonic and quasi-periodic solutions rotating around the origin at different speeds; moreover, this connected set stretches from zero to infinity. The result still holds allowing the force to be attractive only in average provided that an uniformity condition is satisfied and there are no periodic oscillations with zero angular momentum. We provide examples showing that these assumptions cannot be skipped.

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Mathematics Subject Classification: 34C25, 34C27.

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