Geodesic
The Agrachev--Barilari--Boscain Method and Estimates for the Number of Segments of Horizontal Broken Lines Joining Points in the Canonical Carnot Group $G_{3,3}$
Informatics and Automation, Optimal Control and Dynamical Systems, Tome 321 (2023), pp. 108-117.

Voir la notice de l'article provenant de la source Math-Net.Ru

Using a generalization of the Agrachev–Barilari–Boscain method for proving the Rashevskii–Chow theorem, we estimate the minimum number $\mathcal {N}_{G_{3,3}}$ of segments of horizontal broken lines joining two arbitrary points on the six-dimensional two-step canonical Carnot group $G_{3,3}$ with corank $3$ horizontal distribution. We prove that $\mathcal {N}_{G_{3,3}}=3$.
Keywords: canonical Carnot group, Rashevskii–Chow theorem, horizontal broken line. 
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A. V. Greshnov. The Agrachev--Barilari--Boscain Method and Estimates for the Number of Segments of Horizontal Broken Lines Joining Points in the Canonical Carnot Group $G_{3,3}$. Informatics and Automation, Optimal Control and Dynamical Systems, Tome 321 (2023), pp. 108-117. http://geodesic.mathdoc.fr/item/TRSPY_2023_321_a6/

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