Degenerate abnormal trajectories in a sub-Riemannian problem with growth vector (2, 3, 5, 8)


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We consider the nilpotent sub-Riemannian problem with growth vector (2, 3, 5, 8). We describe and study abnormal extremals orthogonal to the cube of the distribution. We analyze the geometric properties of a two-dimensional surface in the state space on which the corresponding abnormal trajectories define optimal synthesis.

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Yu. Sachkov

Steklov Mathematical Institute of the Russian Academy of Sciences; Ailamazyan Program Systems Institute of Russian Academy of Sciences; Peoples Friendship University of Russia

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Email: yusachkov@gmail.com
俄罗斯联邦, Moscow, 119991; Yaroslavskaya oblast, Pereslavskii raion, s. Ves’kovo, 152021; Moscow, 117198

E. Sachkova

Ailamazyan Program Systems Institute of Russian Academy of Sciences

Email: yusachkov@gmail.com
俄罗斯联邦, Yaroslavskaya oblast, Pereslavskii raion, s. Ves’kovo, 152021

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