Geodesic
Discrete symmetries in the generalized Dido problem
Sbornik. Mathematics, Tome 197 (2006) no. 2, pp. 235-257

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The generalized Dido problem is considered — a model of the nilpotent sub-Riemannian problem with the growth vector $(2,\,3,\,5)$. The group of discrete symmetries in this problem is constructed as an extension of the reflection group of the standard mathematical pendulum. The action of these symmetries in the inverse image and image of the exponential map is studied. Bibliography: 16 titles. 
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     author = {Yu. L. Sachkov},
     title = {Discrete symmetries in the generalized {Dido} problem},
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Yu. L. Sachkov. Discrete symmetries in the generalized Dido problem. Sbornik. Mathematics, Tome 197 (2006) no. 2, pp. 235-257. http://geodesic.mathdoc.fr/item/SM_2006_197_2_a6/