Hokkaido University Summer Institute: Introduction to dynamical systems
 Date

2017731 13:30 
201783 16:15
 Place
 4501, Faculty of Science, Hokkaido University

Speaker/Organizer

Part I:31 July, 1 August, 13:0014:30, 14:4516:15, Takao Namiki
The main topics of the lecture are the theory and application on dynamical systems and ergodic theory, especially on symbolic dynamics.
 Basic notions on dynamical systems
 Application: timeseries analysis on brain wave data
 Entropy, topological pressure and variational principle
 Application: fractal geometry and cookiecutter map
Part II: 2 August, 3 August, 13:0014:30, 14:4516:15, Stefano Galatolo
The satistical properties of a dynamical system can be well understood by the study of the associated transfer operator (considered on a suitable function space). In the minicourse following questions will be addressed:
 existence of a regular invariant measure;
 \item Lasota Yorke inequalities and spectral gap;
 \item decay of correlations and some limit theorem;
 \item stability under perturbations of the system.
The point of view taken is to present the general construction and ideas needed to obtain these results in the simplest way, avoiding technicalities. Plan of the lectures:
 Generalities on dynamical systems and ergodic theory. The transfer
operator.
 Regularizing action of the transfer operator on suitable function
spaces. Lasota Yorke inequalities.
 Spectral gap and consequences. Limit theorems.
 Quantitative stability results, Linear response.