射流空间中没有周期性测地线

IF 0.7 3区数学 Q2 MATHEMATICS

Pacific Journal of Mathematics Pub Date : 2022-03-30 DOI:10.2140/pjm.2023.322.11

Alejandro Bravo-Doddoli

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引用次数: 1

摘要

一个实变量$x$的实函数的$k$-射流的$J^k$空间允许亚黎曼流形的结构，该流形具有相关的哈密顿测地流，并且它是可积的。正如在任何哈密顿流中一样，一个自然的问题是周期解的存在性。$J^k$有周期测地线吗？这项研究将找到测地线流在$T^*J^k$中的作用角坐标，并证明$J^k$中的测地线从来都不是周期性的。

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No periodic geodesics in jet space

The $J^k$ space of $k$-jets of a real function of one real variable $x$ admits the structure of a sub-Riemannian manifold, which then has an associated Hamiltonian geodesic flow, and it is integrable. As in any Hamiltonian flow, a natural question is the existence of periodic solutions. Does $J^k$ have periodic geodesics? This study will find the action-angle coordinates in $T^*J^k$ for the geodesic flow and demonstrate that geodesics in $J^k$ are never periodic.

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来源期刊

Pacific Journal of Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Founded in 1951, PJM has published mathematics research for more than 60 years. PJM is run by mathematicians from the Pacific Rim. PJM aims to publish high-quality articles in all branches of mathematics, at low cost to libraries and individuals. The Pacific Journal of Mathematics is incorporated as a 501(c)(3) California nonprofit.