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

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

2010-07-06

arxiv.org/abs/1007.0912v1

Mathematics

Dynamical Systems

Scientific paper

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.

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