SUBJECT

Title

Dynamical systems

Type of instruction

lecture

Level

master

Part of degree program
Credits

3

Recommended in

Semesters 1-4

Typically offered in

Autumn/Spring semester

Course description

Contractions, fixed point theorem. Examples of dynamical systems: Newton’s method, interval maps, quadratic family, differential equations, rotations of the circle. Graphic analysis. Hyperbolic fixed points. Cantor sets as hyperbolic repelleres, metric space of code sequences. Symbolic dynamics and coding. Topologic transitivity, sensitive dependence on the initial conditions, chaos/chaotic maps, structural stability, period three implies chaos. Schwarz derivative. Bifuraction theory. Period doubling. Linear maps and linear differential equations in the plane. Linear flows and translations on the torus. Conservative systems.

Readings
  • B. Hasselblatt, A. Katok: A first course in dynamics. With a panorama of recentdevelopments. Cambridge University Press, New York, 2003.
  • A. Katok, B.Hasselblatt: Introduction to the modern theory of dynamical systems.Encyclopedia of Mathematics and its Applications, 54. Cambridge University Press,Cambridge, 1995.
  • Robert L. Devaney: An introduction to chaotic dynamical systems. Second edition. AddisonWesley Studies in Nonlinearity. AddisonWesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989.