### Periodic data of polar 2-diffeomorphisms with one saddle orbit

Title Periodic data of polar 2-diffeomorphisms with one saddle orbit E. V. Nozdrinova1, O. V. Pochinka11National Research University Higher School of Economics In 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. periodic data, polar diffeomorphism, surface Nozdrinova 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: http://conf.svmo.ru/files/deamm2017/papers/paper58.pdf. - Date of access: 24.10.2020.