Transitive flows on orientable surfaces
- 22 Downloads
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
Unable to display preview. Download preview PDF.
- 9.A. A. Andronov, E. A. Leontovich, and A. G. Maier, Qualitative Theory of Dynamical Systems of the Second Order [in Russian], Nauka, Moscow (1966).Google Scholar
- 11.O. A. Kadubovs’kyi, “Topological equivalence of functions on orientable surfaces,” Ukr. Mat. Zh., 58, No. 3, 343–351 (2006).Google Scholar