Date(s) - 03/11/2015
11 h 00 min - 12 h 00 min
There is a strong and long-lasting interest in chaotic dynamical systems as mathematical models of various processes in different areas of science.
Like for any other mathematical models for chaotic systems to be useful it is desirable that they have stability properties.
There exist different stability properties, “geometric” and “ergodic” ones. I am going to describe some of them in connection with my past and current research. The plan is to discuss the following notions and some relations between them
• Uniform hyperbolicity (strong chaoticiy based on coherent expansion and contraction in all points)
• Structural stability (stability of individual trajectories with respect to a small perturbation of a system as a whole)
• (Inverse) shadowing (stability of trajectories with respect to small per-iteration perturbations)
• Stochastic stability (stability of statistical properties of a system with respect to random per-iteration perturbations)
• Twisted cohomological equations and Weierstrass-like functions (special dynamics-related equations and their solutions of a special kind having interesting properties)
• Linear response (stability and good dependence of statistical properties of a system with respect to a small perturbation of a system as a whole)
I will try to be as short as possible in describing each one so that I have time to cover most.