On realization of Morse-Smale cascades of the sphere of dimension four and higher

Student: Smirnova Anna

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

Educational Programme: Mathematics (Bachelor)

Final Grade: 8

Year of Graduation: 2020

The present work is devoted to solving the problem of realization of topological conjugacy classes for the class of Morse-Smale diffeomorphisms on a sphere of dimension greater than three such that the invariant varieties of different saddle periodic points do not intersect. In this paper the properties of two-colored draphs of diffeomorphisms are studied, the set of admissible graphs is described, and an algorithm of realization the simplest admissible graph and its аrbitrary automorphism is described. The algorithm is brought to a computer implementation in Python.

Full text (added May 14, 2020)

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