Abstract
We consider a convex Lagrangian
$L:\mathit{TM}\rightarrow \mathbb{R}$
quadratic at infinity with
$L(x,0)=0$
for every
$x\in M$
and such that the 1-form
$\unicode[STIX]{x1D703}$
defined by
$\unicode[STIX]{x1D703}_{x}(v)=L_{v}(x,0)v$
is not closed. We show that for every number
$a<0$
, there is a contractible (nonconstant) periodic orbit with action
$a$
. We also obtain estimates of the period and energy of such periodic orbits.
Publisher
Cambridge University Press (CUP)
Cited by
1 articles.
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