ODE trajectories as abnormal curves in Carnot groups

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:300

Article

Hakavuori, Eero¹ 

[1] SISSA, Via Bonomea 265, I-34136 Trieste, Italy

关键词: Carnot groups;    Sub-Riemannian geometry;    Abnormal extremals;   

DOI  :  10.1016/j.jde.2021.07.046

来源: Elsevier

【 摘 要 】

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. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free