# American Institute of Mathematical Sciences

January  2011, 29(1): 169-192. doi: 10.3934/dcds.2011.29.169

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

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

Received  November 2009 Revised  February 2010 Published  September 2010

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.
Citation: Alessandro Fonda, Antonio J. Ureña. Periodic, subharmonic, and quasi-periodic oscillations under the action of a central force. Discrete & Continuous Dynamical Systems - A, 2011, 29 (1) : 169-192. doi: 10.3934/dcds.2011.29.169
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