Ergodic theory

Summary

This is an introductory course in ergodic theory, providing a comprehensive overlook over the main aspects and applications of this field.

Content

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Keywords

ergodic theory, dynamcial systems, measure-preserving transformation, entropy

Learning Prerequisites

Recommended courses

Measure and integration

Important concepts to start the course

This course is aimed at master's or advanced bachelor's students. Since ergodic theory is largely based on the notions of measure theory, either some background in measure theory or the willingness to learn some of this material along the way is expected. I will provide a handout summarizing the prerequisites from measure theory that are needed for this course at the beginning of the semester.

Learning Outcomes

By the end of the course, the student must be able to:

• Formalize dynamcial ideas and concepts such as ergodicity, entropy, chaos, determinism, etc.
• Apply tools and techniques from ergodic theory in other areas
• Interpret examples of dynamical systems
• Prove results in ergodic theory

Transversal skills

• Use a work methodology appropriate to the task.
• Demonstrate a capacity for creativity.
• Demonstrate the capacity for critical thinking
• Continue to work through difficulties or initial failure to find optimal solutions.

Teaching methods

in-person lectures, in-person exercise sessions with the teaching assistant

Assessment methods

oral exam

Supervision

Office hours	No
Assistants	Yes
Forum	Yes

Resources

Bibliography

• M. Einsiedler, T. Ward, Ergodic Theory with a view towards Number Theory, Springer-Verlag London, 2011.
• P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, Springer New York, 1982.

Ressources en bibliothèque

• An Introduction to Ergodic Theory / Walters
• Ergodic Theory with a view towards Number Theory / Einsiedler

Notes/Handbook

Lecture notes will be provided

Moodle Link

• https://go.epfl.ch/MATH-518