@article {2012,
	title = {On a class of vector fields with discontinuity of divide-by-zero type  and its applications},
	journal = {Journal of dynamical and control systems },
	volume = {18},
	number = {arXiv:1007.0912;},
	year = {2012},
	pages = {135-158},
	publisher = {Springer},
	abstract = {<p>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.</p>},
	doi = {10.1007/s10883-012-9137-4},
	author = {Roberta Ghezzi and Alexey O. Remizov}
}
