EVENT DETAILS AND ABSTRACT

Title: Shadowing in smooth flows and structural stability.
Speaker: Professor Sergey Tikhomirov
Speaker Info: Saint Petersburg University
Brief Description:
Special Note:
Abstract:

The shadowing problem is related to the following question: under which condition, for any pseudotrajectory (approximate trajectory) of a vector field there exists a close trajectory? We study $C^1$-interiors of sets of vector fields with various shadowing properties. In the case of discrete dynamical systems generated by diffeomorphisms, such interiors were proved to coincide with the set of structurally stable diffeomorphisms for most general shadowing properties.

We prove that the $C^1$-interior of the set of vector fields with oriented shadowing property contains not only structurally stable vector fields. Also, we have found additional assumptions under which the $C^1$-interiors of sets of vector fields with Lipschitz, Oriented and Orbit shadowing properties contain only structurally stable vector fields.

Some of these results were obtained together with my advisor S.Yu.Pilyugin.