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 | References | Similar Articles | Additional Information

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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Additional Information

**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

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.