M7960 Dynamical Systems

Faculty of Science
Spring 2011 - only for the accreditation
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction in the modern theory of dynamical systems.
At the end of the course students should be able to understand the concept of dynamic system (discrete and continuous), and the main techniques used for analysis of such systems.
Syllabus
  • Dynamics in Nature and Mathematics,
  • one-dimensional dynamics by iterations (quadratic maps),
  • reccurence and chaos (Sharkovski's Theorem),
  • analysis near fixed points (Hartman-Grobman Theorem, invariant manifolds),
  • analysis near periodic solution,
  • hyperbolic attractors (shifts, horseschoe, solenoid attractor, Lorenz attractor).
Literature
  • KATOK, A. B., Boris HASSELBLATT and Leonardo MENDOZA. Introduction to the modern theory of dynamical systems. Cambridge: Cambridge University Press, 1995, xviii, 802. ISBN 0521341876. info
Teaching methods
Lectures
Assessment methods
Oral exam
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.