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Periodic Data of Diffeomorphisms of a Two-Dimensional Sphere with a Single Saddle Orbit

Student: Leonov Denis

Supervisor: Olga Pochinka

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

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2019

In this paper we consider the class G of gradient-like orientation-preserving diffeomorphisms of a 2-sphere with saddles of negative orientation type. It is shown that for every diffeomorphism from the class G each saddle point is fixed. Up to topological conjugacy, there are only three equivalence classes. The main result of the paper is the proof of the fact that any diffeomorphism from class G is connected by a stable arc with a source-sink diffeomorphism. At the same time, the arc passes through a finite number of flip bifurcations.

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