ODE trajectories as abnormal curves in Carnot groups

2020/06/17 by Hakavuori, Eero
#22E25 #37N35 #53C17 #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.09783

Abstract

We prove that for every polynomial ODE there exists a Carnot group where the trajectories of the ODE lift to abnormal curves. The proof defines an explicit construction to determine a covector for the resulting abnormal curves. Using this method we give new examples of abnormal curves in Carnot groups of high step. As a byproduct of the argument, we also prove that concatenations of abnormal curves have abnormal lifts.

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