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.