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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Periodic solutions of radially symmetric perturbations of Newtonian systems


Authors: Alessandro Fonda and Rodica Toader
Journal: Proc. Amer. Math. Soc. 140 (2012), 1331-1341
MSC (2010): Primary 34C25
Published electronically: August 3, 2011
MathSciNet review: 2869116
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Abstract: The classical Newton equation for the motion of a body in a gravitational central field is here modified in order to include periodic central forces. We prove that infinitely many periodic solutions still exist in this case. These solutions have periods which are large integer multiples of the period of the forcing and rotate exactly once around the origin in their period time.


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Alessandro Fonda
Affiliation: Dipartimento di Matematica e Informatica, Università di Trieste, Piazzale Europa 1, I-34127 Trieste, Italy
Email: a.fonda@units.it

Rodica Toader
Affiliation: Dipartimento di Ingegneria Civile e Architettura, Università di Udine, Via delle Scienze 208, I-33100 Udine, Italy
Email: toader@uniud.it

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10992-4
PII: S 0002-9939(2011)10992-4
Keywords: Periodic solutions, Newton’s equation, nonlinear dynamics
Received by editor(s): November 30, 2009
Received by editor(s) in revised form: January 4, 2011
Published electronically: August 3, 2011
Communicated by: Yingei Yi
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.