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Periodic orbits with prescribed abbreviated action


Author: Miguel Paternain
Journal: Proc. Amer. Math. Soc. 143 (2015), 4001-4008
MSC (2010): Primary 37JXX, 70HXX
DOI: https://doi.org/10.1090/S0002-9939-2015-12597-X
Published electronically: March 18, 2015
MathSciNet review: 3359588
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Abstract: We show that for every convex Lagrangian quadratic at infinity there is a real number $ w_0$ such that for every $ w>w_0$ the Lagrangian has a periodic orbit with abbreviated action $ w$.


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Additional Information

Miguel Paternain
Affiliation: Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, Uruguay
Email: miguel@cmat.edu.uy

DOI: https://doi.org/10.1090/S0002-9939-2015-12597-X
Keywords: Convex Lagrangian, action functional, periodic orbit, Ma\~n\'e's critical value
Received by editor(s): May 29, 2014
Published electronically: March 18, 2015
Additional Notes: The author was supported by an Anii grant
Communicated by: Yingfei Yi
Article copyright: © Copyright 2015 American Mathematical Society