Nonlinear Oscillations

, Volume 9, Issue 2, pp 173–180 | Cite as

Transitive flows on orientable surfaces

  • O. A. Kadubovs’kyi


We consider smooth vector fields on closed orientable surfaces with a fixed collection of singularities and a finite number of separatrices none of which connects the equilibrium states. We prove that, on an orientable surface of arbitrary genus g ≥ 2, there exists a vector field with an admissible set of singularities (degenerate saddles) whose trajectory is everywhere dense on the surface.


Orientable Surface Morse Function Cyclic Order Periodic Trajectory Transitive Flow 
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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • O. A. Kadubovs’kyi
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKyiv

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