The aim of this School is to introduce undergraduate and PhD students in Mathematics and Its Applications as well as postdoctoral researchers to a fast developing branch of the global theory of dynamical systems, theory of shadowing of approximate trajectories (pseudotrajectories).
During computer modeling, round-of errors, errors of numerical methods, etc, result in getting approximate trajectories of the studied process instead of exact trajectories.
The theory of shadowing of approximate trajectories in dynamical systems is aimed at the following problem:
For which systems, approximate trajectories are close to exact ones on unbounded time intervals? In other words, the aim is to understand whether the pattern of trajectories of the considered process resulting from the computer output reflects the real pattern.
This is directly related to the very important problem of reliability of computer modeling.
The lectures will be given by the author of the first book on shadowing in the world mathematical literature:
Sergei Yu. Pilyugin. Shadowing in Dynamical Systems, Lect. Notes in Math., vol. 1706, Springer-Verlag (1999).