Geodesic
Front Asymptotics of a Flat Sub-Riemannian Structure on the Engel Distribution
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Dynamical Systems, Tome 321 (2023), pp. 62-76

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We approximate the front of a flat sub-Riemannian structure on the Engel distribution in a neighborhood of a non-subanalytic singularity by the front of a control system integrable in elementary functions. As a corollary, we find the asymptotics of the exponential map of a flat sub-Riemannian structure on the Engel distribution.
Keywords: sphere and front of a sub-Riemannian structure, Engel distribution, exponential map. 
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     author = {I. A. Bogaevsky},
     title = {Front {Asymptotics} of a {Flat} {Sub-Riemannian} {Structure} on the {Engel} {Distribution}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {62--76},
     publisher = {mathdoc},
     volume = {321},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2023_321_a3/}
}
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I. A. Bogaevsky. Front Asymptotics of a Flat Sub-Riemannian Structure on the Engel Distribution. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Dynamical Systems, Tome 321 (2023), pp. 62-76. http://geodesic.mathdoc.fr/item/TM_2023_321_a3/