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Periodic orbits of Lagrangian systems with prescribed action or period

Author: Miguel Paternain
Journal: Proc. Amer. Math. Soc. 144 (2016), 2999-3007
MSC (2010): Primary 37JXX; Secondary 70HXX
Published electronically: January 26, 2016
MathSciNet review: 3487231
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Abstract: We show that for every convex Lagrangian quadratic at infinity there is a real number $ a_0$ such that for every $ a>a_0$ the Lagrangian has a periodic orbit with action $ a$. We attain estimates on the period and energy of the periodic orbits obtained. We also show that such a Lagrangian has periodic orbits of every period.

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Additional Information

Miguel Paternain
Affiliation: Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, Uruguay

Keywords: Convex Lagrangian, action functional, periodic orbit
Received by editor(s): April 28, 2015
Received by editor(s) in revised form: August 10, 2015, and August 31, 2015
Published electronically: January 26, 2016
Additional Notes: The author was supported by an Anii grant
Communicated by: Yingfei Yi
Article copyright: © Copyright 2016 American Mathematical Society

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