2023/2024

Introduction to Ergodic Theory

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

When: 1, 2 module

Open to: students of all HSE University campuses

Instructors: Mikhail Blank

Language: English

ECTS credits: 3

Contact hours: 30

Course Syllabus

Abstract

Is it possible to distinguish deterministic chaotic dynamics from a purely random and whether this question makes sense? Does irreversibility influence qualitative characteristics of the process? Ergodic theory studies these and other statistical properties of dynamical systems. Interest in this subject stems from the fact that «typical» deterministic dynamical systems (eg, differential equations) exhibit chaotic behavior: their trajectories look similar to the implementation of random processes. We begin with the classical results by Poincare, Birkhoff, Khinchin, Kolmogorov, and get to modern productions (including yet unresolved) problems. This is an introductory course designed for 2 – 4 bachelors and graduate students. Prior knowledge except for the course in mathematical analysis is not required (although it is desirable). PREREQUISITES: calculus.