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Pré-Publication, Document De Travail Année : 2010

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

Résumé

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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Dates et versions

hal-00496813 , version 1 (05-07-2010)

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Roberta Ghezzi, Alexey Remizov. On a class of vector fields with discontinuity of divide-by-zero type and its applications. 2010. ⟨hal-00496813⟩
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