Transitive flows on orientable surfaces
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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.
KeywordsOrientable Surface Morse Function Cyclic Order Periodic Trajectory Transitive Flow
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