Periodic data of polar 2-diffeomorphisms with one saddle orbit

TitlePeriodic data of polar 2-diffeomorphisms with one saddle orbit
AuthorsE. V. Nozdrinova1, O. V. Pochinka1
1National Research University Higher School of Economics
AnnotationIn this paper we consider polar diffeomorphisms of a surface, that is, diffeomorphisms having a unique sink and a unique source periodic orbit. A classical example of such a diffeomorphism is the ``source-sink'' diffeomorphism, which does not have saddle points and exists only on a two-dimensional sphere. However, the addition of even a one saddle orbit will significantly expand the class of the polar diffeomorphisms on surfaces. In particular, in this paper the authors proved that polar diffeomorphisms with exactly one saddle orbit there are on arbitrary surface and the saddle orbit always has a negative orientation type. In addition, all possible types of periodic data for such polar diffeomorphisms are established.
Keywordsperiodic data, polar diffeomorphism, surface
CitationNozdrinova E. V., Pochinka O. V. ''Periodic data of polar 2-diffeomorphisms with one saddle orbit'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 408-417. Available at: https://conf.svmo.ru/files/deamm2017/papers/paper58.pdf. - Date of access: 22.06.2024.