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No Periodic normal Geodesics in Jk(ℝ,ℝn)

2022/05/12 by Alejandro Bravo-Doddoli, Bravo-Doddoli, Alejandro
Mathematics · #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.2205.06156

openalex publication_date 2022/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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