Math Seminars

Vadim Kaloshin
(PSU)

Newton Interpolation, Discretization method, and certain prevalent properties of dynamical systems


I will describe a general method of studying prevalent properties of diffeomorphisms of a compact manifold. The method is based on discretization of dynamics: splitting the set of all trajectories of finite length into a finite set of pseudo-trajectories. Then to analyze prevalent properties of those we use Newton Interpolation Polynomials. Application growth of the number of periodic points and finiteness of the number of coexisting sinks (Newhouse phenomenon) will be presented. This is based on a joint work with B. Hunt and A. Gorodetski.