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On a class of vector fields with discontinuity of divide-by-zero type and its applications

TitleOn a class of vector fields with discontinuity of divide-by-zero type and its applications
Publication TypeJournal Article
Year of Publication2012
AuthorsGhezzi, R, Remizov, AO
JournalJournal of dynamical and control systems 18, nr. 1 (2012) 135-158
Abstract

We study phase portraits and singular points of vector fields of a special
type, that is, vector fields whose components are fractions with a common
denominator vanishing on a smooth regular hypersurface in the phase space. We assume also some additional conditions, which are fulfilled, for instance, if the vector field is divergence-free. This problem is motivated by a large number of applications. In this paper, we consider three of them in the framework of differential geometry: singularities of geodesic flows in various singular metrics on surfaces.

DOI10.1007/s10883-012-9137-4

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