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Еrgodic theory

2021/2022
Academic Year
ENG
Instruction in English
5
ECTS credits

Instructor

Course Syllabus

Abstract

The course “Ergodic Theory” is aimed for introducing the students to the modern state and problems of dynamical systems having complicated (chaotic) behavior. Such systems usually can be described and studied with the help of Ergodic Theory.
Learning Objectives

Learning Objectives

  • To show the actual state of studying complicated dynamical systems using invariant measures and dynamical invariants which are responsible for complexity of the system. To explain the phenomena of limit behavior of chaotic systems and its relation to the evolution limits of probability distributions in ergodic theorems ( the results going back to the results of Poincare, Birkhoff, , Khinchin, Krylov, Bogolyubov, Kolmogorov, Sinai). To provide constructions and methods for modeling invariant measures and computing the invariants for concrete dynamical systems..
Expected Learning Outcomes

Expected Learning Outcomes

  • Knowledge of classical Ergodic theorems
  • Understanding the constructions of invariant measures
  • Understanding the constructions of Symbolic Dynamics.
  • Understanding the relationship between topological dynamics and Ergodic Theory.
  • Understanding the relationship between topological dynamics and Ergodic Theory.
Course Contents

Course Contents

  • Symbolic Dynamics
  • Entropic Theory of Discrete Dynamical Systems.
  • Classical Theorems of Ergodic Theory. Ergodic Theory of Low Dimensional Systems.
Assessment Elements

Assessment Elements

  • non-blocking Реферат
  • non-blocking Экзамен
Interim Assessment

Interim Assessment

  • 2021/2022 3rd module
    0.5 * Реферат + 0.5 * Экзамен
  • 2021/2022 4th module
    0.5 * Реферат + 0.5 * Экзамен
Bibliography

Bibliography

Recommended Core Bibliography

  • Hasselblatt, Boris. Ergodic Theory and Negative Curvature [Электронный ресурс] / Boris Hasselblatt; БД springer. - Springer, Cham, 2017 - ISBN: 978-3-319-43058-4 (Print).

Recommended Additional Bibliography

  • . Kuznetsov, Sergey. Strange Nonchaotic Attractors : Dynamics Between Order and Chaos in Qua-siperiodically Forced Systems [Электронный ресурс] / Sergey Kuznetsov, Arkady Pikovsky, and Ul-rike Feudel. – World Scientific Publishing Co Pte Ltd, 2014, . – ISBN: 9789812566331 (Print).