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

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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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     author = {A. V. Greshnov},
     title = {The {Agrachev--Barilari--Boscain} {Method} and {Estimates} for the {Number} of {Segments} of {Horizontal} {Broken} {Lines} {Joining} {Points} in the {Canonical} {Carnot} {Group} $G_{3,3}$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {108--117},
     publisher = {mathdoc},
     volume = {321},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/TM_2023_321_a6/}
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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 $G_{3,3}$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Dynamical Systems, Tome 321 (2023), pp. 108-117. http://geodesic.mathdoc.fr/item/TM_2023_321_a6/