The Maxwell set in the generalized Dido problem

The generalized Dido problem is considered — a model of the nilpotent sub-Riemannian problem with the growth vector $(2,3,5)$. We study the Maxwell set, that is, the locus of the intersection points of geodesics of equal lengths. A general description is obtained for the Maxwell strata corresponding to the symmetry group of the exponential map generated by rotations and reflections. The invariant and graphic meaning of these strata is clarified.
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