Periodic orbits of Lagrangian systems with prescribed action or period

Paternain, Miguel

doi:10.1090/proc/12950

Periodic orbits of Lagrangian systems with prescribed action or period
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Proc. Amer. Math. Soc. 144 (2016), 2999-3007 Request permission

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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