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The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry

TitleThe sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry
Publication TypeJournal Article
Year of Publication2011
AuthorsBonnard, B, Charlot, G, Ghezzi, R, Janin, G
JournalJournal of Dynamical and Control Systems 17 (2011) 141-161
Abstract

We study the tangential case in 2-dimensional almost-Riemannian geometry. We\\r\\nanalyse the connection with the Martinet case in sub-Riemannian geometry. We\\r\\ncompute estimations of the exponential map which allow us to describe the\\r\\nconjugate locus and the cut locus at a tangency point. We prove that this last\\r\\none generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.

URLhttp://hdl.handle.net/1963/4914
DOI10.1007/s10883-011-9113-4

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