MATH-523 / 5 credits

Teacher: Krieger Joachim

Language: English

## Summary

An introduction to some key concepts and theorems from dynamical systems, including discrete dynamical systems as well as flows.

## Content

-abstract dynamical systems

-ergodicity

-Poincare recurrence

-Birkhoff theorem

-invariant manifolds and hyperbolicity

-Conjugation problem

-Poincare-Bendixson theory.

## Required courses

Analysis I - IV, Algebre Lineaire I and II.

## Recommended courses

Analysis I - IV, Algebre Lineaire I and II.

## Important concepts to start the course

Understand key concepts of real analysis, such as measure and Lebesgue integral. Some familiarity with Fourier series and ordinary differential equations. Be able to construct a rigorous mathematical argument.

## Learning Outcomes

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

• Analyze abstract dynamical systems
• Examine issues concerning the local and global behavior of dynamical systems
• Prove basic results, such as Poincare recurrence.
• Contrast different dynamical behaviors.

Oral exam

## Supervision

 Office hours No Assistants Yes Forum No

No

## In the programs

• Semester: Fall
• Exam form: Oral (winter session)
• Subject examined: Introduction to dynamical systems
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Oral (winter session)
• Subject examined: Introduction to dynamical systems
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Oral (winter session)
• Subject examined: Introduction to dynamical systems
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Fall
• Exam form: Oral (winter session)
• Subject examined: Introduction to dynamical systems
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional

## Reference week

Friday, 10h - 12h: Lecture MEB331

Friday, 13h - 15h: Exercise, TP MEB331

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