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CONTRACTIBLE PERIODIC ORBITS OF LAGRANGIAN SYSTEMS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 99 / Issue 3 / June 2019
- Published online by Cambridge University Press:
- 30 January 2019, pp. 445-453
- Print publication:
- June 2019
-
- Article
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- You have access
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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.
