On Interrelations Between Trivial and Nontrivial Basic Sets of Structurally Stable Diffeomorphisms of Surfaces

Student: Mints Dmitrii

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

Educational Programme: Mathematics (Bachelor)

Final Grade: 10

Year of Graduation: 2021

This graduate work is devoted to the interrelations between the existence of trivial and nontrivial basic sets of A-diffeomorphisms of surfaces. It is proved that if all trivial basic sets of a structurally stable diffeomorphism of a closed surface are source periodic points $\alpha_1, ...,\alpha_k$, then the non-wandering set of this diffeomorphism consists of points $\alpha_1, ...,\alpha_k$ and exactly one one-dimensional attractor $\ Lambda$. Sufficient conditions for the attractor $\Lambda$ to be widely situated are given. It is also proved that if the non-wandering set of a structurally stable diffeomorphism of a closed surface contains a nontrivial zero-dimensional basic set, then it also contains source and sink periodic points.

Full text (added May 25, 2021)

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