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On Realization of Gradient-Like Diffomorphisms of Two Dimensional

Student: Ekaterina Sablina

Supervisor: Elena Gurevich

Faculty: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2020

Let G(S^2) be the class of gradient-like diffeomorphisms on the sphere. We study periodic data of diffeomorphisms f in G(S^2), that is interrelation between numbers of sink, source and saddle orbits. Then we provide a notion of admissible periodic set and solve the problem of realization. It means that for any given admissible periodic set we construct a diffeomorphism from the class G(S^2) whose periodic data coincides with the admissible periodic set.

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