【学部向け(数学総合講義I)/大学院向け(大学院共通授業)】「力学系入門」

開催日時
2017年   7月 31日 ~ 2017年   8月 3日
場所
4-501, Dept. Math, Hokkaido University
講演者
Takao Namiki, Stefano GALATOLO
 

Part I:31 July, 1 August, 13:00-14:30, 14:45-16:15, 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: time-series analysis on brain wave data

  • Entropy, topological pressure and variational principle

  • Application: fractal geometry and cookie-cutter map


Part II: 2 August, 3 August, 13:00-14:30, 14:45-16:15, 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;

  • Lasota Yorke inequalities and spectral gap;

  • decay of correlations and some limit theorem;

  • 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:

  1. Generalities on dynamical systems and ergodic theory. The transfer
    operator.

  2. Regularizing action of the transfer operator on suitable function
    spaces. Lasota Yorke inequalities.

  3. Spectral gap and consequences. Limit theorems.

  4. Quantitative stability results, Linear response.



関連項目

研究集会・セミナー・集中講義の一覧へ