Dynamical Systems
(Lecture Course 2 hrs/week)
(click here for German Version)
Current Situation: Due to the "Corona" requirement to offer courses and to interact merely in the virtual digital space, this lecture course, its web page and its optional seminar is under construction for a while.
I am currently still working on finding, developing and implementing additional alternative formats.
Part of this is will be the university's MOODLE platform.
Please consult frequently the subordinate link for current announcements.
This course is also part of the module 10-MAT-MPDS1 in the International Master of Science Program "Mathematical Physics". Hence, the course language is English.
Along with this course, there is the Seminar "Dynamical Systems". This seminar extends the lecture course and seminar participation requires participation in this lecture course.
The converse is not true: Participation in the lecture course does not require participation in the seminar.
Starting date for the lectures the online program: expected 06.04.20
Starting date for the Seminar: expected 13.04.20
both on Moodle!
Target Group:
- Students in the Diploma Programs of
Mathematik und Wirtschaftsmathematik
in 4th or 6th semester, and
- students enrolled in the international program MSc Mathematical Physics, 2nd semester of 1st year
Scope: The theoretical field of dynamical systems is quite broad, too broad for one 2hr course.
In this lecture course, we will give a short general introduction to dynamical systems and will then focus primarily on the measure-theoretical side of dynamical systems. Among other notions, a major object of interest is the notion of entropy in the dynamical context, in both its versions of topological and measure-theoretical entropy. Also, basic aspects of ergodic theory will be introduced.
Literature:
- L. Barreira, Ergodic Theory, Hyperbolic Dynamics and Dimension Theory, Universitext, Springer, 2012
- M. Policott a. M. Yuri, Dynamical Systems and Ergodic Theory, LMS Student Texts 40, Cambridge Univ. Press, 1998
- A. Katok a. B. Hasselblatt, Introduction to the modern theory of dynamical systems, Cambridge Univ. Press, 1995
- Y. Sinai, Topics in Ergodic Theory, Princeton Univ. Press 1994
- E. Zehnder, Lectures on Dynamical Systems, EMS Textbooks in Mathematics, European Mathematical Society, 2010
- (unfortunately only available in German: M. Denker, Einführung in die Analysis dynamischer Systeme, Springer-Verlag 2005)
Requirements:
- no formal requirements, but advisable are
- sufficient skills in analysis and measure theory
(e.g. semesters 1-3 in diploma programs, or modules 12-PHY-MPMP1 and 12-PHY-MPMP2)
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