Research of manifolds of Morse-Smale diffeomorphisms

About ongoing research.

In the framework of joint research with leading scientists of the International laboratory of dynamical systems and applications of the HSE, since February 2020, a study on the topic of the megagrant "Theory of dynamical systems and applications" was conducted by performers E.V. Zhuzhoma and V.S. Medvedev.

We describe the topological structure of closed manifolds of dimension at least four on which there are Morse-Smale diffeomorphisms such that their non-wandering set contains an arbitrary number of stock periodic points, an arbitrary number of source periodic points, and two saddle periodic points. We also describe the carrier manifolds of Morse-Smale diffeomorphisms with fewer saddle periodic points.

Based on the results of the research, an article "On carrier manifolds of multidimensional Morse-Smale diffeomorphisms with two saddle periodic points" was prepared and sent to the journal "Mathematical Notes".