论文标题
$ j^k（\ mathbb {r}，\ mathbb {r}^n）$ in $ j^k（\ mathbb {r}中没有周期性的普通测量学
No Periodic normal Geodesics in $J^k(\mathbb{R},\mathbb{R}^n)$
论文作者
论文摘要
$ n $ $ n $的$ k $ jets的空间一个真实变量$ x $的真实功能承认了一个Carnot组的结构，然后它具有相关的Hamiltonian Geodesic Flow。就像在任何哈密顿流动中一样，一个自然的问题是周期性解决方案的存在。 $ k $ - 喷气机的空间是否具有定期的测量学？这项研究将证明次级测量流的整合性，在$ k $ -Jets的空间中表征和分类，并将其分类为$ k $ -Jets，并表明它们从不定期。
The space of $k$-jets of $n$ real function of one real variable $x$ admits the structure of a Carnot group, which then has an associated Hamiltonian geodesic flow. As in any Hamiltonian flow, a natural question is the existence of periodic solutions. Does the space of $k$-jets have periodic geodesics? This study will demonstrate the integrability of subRiemannian geodesic flow, characterize and classify the subRiemannian geodesics in the space of $k$-jets, and show that they are never periodic.
