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Classification of suspensions over Cartesian products of orientation-changing diffeomorphisms of the circle

TitleClassification of suspensions over Cartesian products of orientation-changing diffeomorphisms of the circle
AuthorsS. K. Zinina1
1National Research Mordovia State University
AnnotationThe paper introduces a class of Cartesian products of orientation-changing rough transformations of a circle, and studies their dynamics. The structure of the set of periodic points is described in detail, and a theorem on the topological conjugacy of diffeomorphisms of the class under consideration is given. In the theory of smooth dynamical systems, a construction is very useful that allows, according to a given diffeomorphism of a f manifold, to construct a flow on a manifold with a dimension one greater, this flow is called a superstructure over f. The concept of a superstructure over diffeomorphisms of the class under consideration is introduced, various types and the number of orbits of the superstructure are described; a theorem on the topology of the manifold on which the superstructure is given is proved. For the topological equivalence of the superstructures over the diffeomorphisms of our class, the topological conjugacy of the diffeomorphisms over which the superstructures are taken is necessary and sufficient.
Keywordsdiffeomorphisms of a circle, orientation-changing diffeomorphisms of a circle, Cartesian product of orientation-changing diffeomorphisms of a circle, superstructure over a diffeomorphism, topological classification of diffeomorphisms
CitationZinina S. K. ''Classification of suspensions over Cartesian products of orientation-changing diffeomorphisms of the circle'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 14-18, 2022). Saransk: SVMO Publ, 2022. - pp. 100-103. Available at: https://conf.svmo.ru/files/2022/papers/paper15.pdf. - Date of access: 30.11.2022.