Open AccessPeriodic orbits of Lagrangian systems with prescribed action or period
Author(s) -
Miguel Paternain
Publication year - 2016
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/12950
Subject(s) - algorithm , annotation , computer science , artificial intelligence
We show that for every convex Lagrangian quadratic at infinity there is a real number a 0 a_0 such that for every a > a 0 a>a_0 the Lagrangian has a periodic orbit with action a 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.