ODE trajectories as abnormal curves in Carnot groups
Differential Geometry
2020-06-18 v1 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.2006.09783,
title = {ODE trajectories as abnormal curves in Carnot groups},
author = {Eero Hakavuori},
journal= {arXiv preprint arXiv:2006.09783},
year = {2020}
}
Comments
31 pages, 5 figures