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arXiv · 2203.16178

No Periodic Geodesics in Jet Space

Alejandro Bravo-Doddoli
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Abstract

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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Alejandro Bravo-Doddoli. 2022-03-30. No Periodic Geodesics in Jet Space. https://doi.org/10.2140/pjm.2023.322.11

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