Ergodic theory and dynamical systems 1000-1S24TEUD
In the ergodic theory of Dynamical Systems, one studies the time evolution of various systems, with an emphasis on stochastic properties and geometry of limit sets.
During the seminar, we are going to present elements of the dynamical systems theory in many examples. We will study iterations of the maps of the circle, interval, complex plane, smooth maps on manifolds and measure-preserving transformations. The main focus of interest will be the study of geometric and ergodic (stochastic) aspects of various systems.
The seminar has been running for many years at the Faculty of Mathematics, Informatics and Mechanics of the Warsaw University. The talks during the seminar are presented by participating students and guests from other universities and research centers from Poland and other countries. In the presence of foreign participants the seminar is run in English.
Main fields of studies for MISMaP
computer science
physics
Type of course
Mode
Prerequisites (description)
Course coordinators
Learning outcomes
Acquiring basic knowledge on dynamical systems nad ergodic theory. Ability to analyze simple dynamical systems in respect to their geometric and stochastic properties.
Assessment criteria
Regular attendance at the meetings of the seminar. Preparing and presenting at least one talk on a given topic during each semester.
Bibliography
M. Brin, G. Stuck, Introduction to Dynamical Systems, Cambridge University Press, Cambridge, 2004.
R. Devaney, An introduction to chaotic dynamical systems, third edition, CRC Press, Boca Raton, 2022
S. Fomin, I. Kornfeld, J. Sinaj, Teoria ergodyczna, Państwowe Wydawnictwo Naukowe, Warszawa, 1987.
M. Pollicott, M. Yuri, Dynamical systems and ergodic theory, London Mathematical Society Student Texts, 40, Cambridge University Press, Cambridge, 1998.
F. Przytycki, M. Urbański, Conformal fractals. Ergodic theory methods, London Mathematical Society Lecture Note Series 371, Cambridge University Press, Cambridge, 2010.
C. Robinson, Dynamical systems. Stability, symbolic dynamics and chaos, Second edition, CRC Press, Boca Raton, 1999.
W. Szlenk, Wstęp do teorii gładkich układów dynamicznych, Państwowe Wydawnictwo Naukowe, Warszawa, 1982.
P. Walters, An introduction to ergodic theory, Springer-Verlag, New York-Berlin, 1982.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: