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CONTRACTIBLE PERIODIC ORBITS OF LAGRANGIAN SYSTEMS
Published online by Cambridge University Press: 30 January 2019
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.
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- Research Article
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- © 2019 Australian Mathematical Publishing Association Inc.
Footnotes
The author was supported by an Anii grant.
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