International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 185-196

Vector fields generating more than one flow

Slawomir Dorosiewicz1 and Kazimierz Napiórkowski2

1Institute of Econometry, Central School of Planning and Statistics, AI. Niepodległości 162, Warsaw 02-519, Poland
2Department of Mathematical Methods in Physics, Warsaw University, Hoźa 74, Warsaw 00-682, Poland

Received 18 February 1993; Revised 19 July 1993

Copyright © 1995 Slawomir Dorosiewicz and Kazimierz Napiórkowski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Vector fields generating more than one flow on a manifold are constructed. For one-dimensional case a complete description of the set of flows is given. For dimensions larger than one a method of constructing vector fields with dense or open branched sets sets is given. Density of vector fields with nonempty sets of branched points is studied.