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

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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.

fields

cs.CL 1

years

2025 1

verdicts

CONDITIONAL 1

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