Spiraling of sub-Riemannian geodesics around the Reeb flow in the 3D contact case - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2021

Spiraling of sub-Riemannian geodesics around the Reeb flow in the 3D contact case

Luc Hillairet

Abstract

We consider a closed three-dimensional contact sub-Riemannian manifold. The objective of this note is to provide a precise description of the sub-Riemannian geodesics with large initial momenta: we prove that they "spiral around the Reeb orbits", not only in the phase space but also in the configuration space. Our analysis is based on a normal form along any Reeb orbit due to Melrose.
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Dates and versions

hal-03151365 , version 1 (24-02-2021)

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  • HAL Id : hal-03151365 , version 1

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Yves Colin de Verdière, Luc Hillairet, Emmanuel Trélat. Spiraling of sub-Riemannian geodesics around the Reeb flow in the 3D contact case. 2021. ⟨hal-03151365⟩
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