Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

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
DOI: https://doi.org/10.1090/proc/12950
Published electronically: January 26, 2016
MathSciNet review: 3487231
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 37JXX, 70HXX

Retrieve articles in all journals with MSC (2010): 37JXX, 70HXX


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/proc/12950
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