CONTRACTIBLE PERIODIC ORBITS OF LAGRANGIAN SYSTEMS

PATERNAIN MIGUEL
Bulletin of the Australian Mathematical Society . 2019, 99 (03), 445-453;
http://dx.doi.org/10.1017/s0004972718001624 | Referencias: 19

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...Leer más