Instructor: Dr. Zoltán BUCZOLICH
- Robert L. Devaney: An introduction to chaotic dynamical systems. Second edition. Addison Wesley Studies in Nonlinearity. Addison Wesley
- B. Hasselblatt, A. Katok: A first course in dynamics. With a panorama of recent developments. 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.
Prerequisits: A standard course in Calculus I and II. Some knowledge of metric spaces and differential equations.
The purpose of the course to introduce basic concepts and examples of Dynamical Systems.
Topics: Contractions, fixed point theorems. Examples of Dynamical Systems: Newton's method, interval maps, the quadratic family, differential equations, rotations of the circle. graphical analysis. Hyperbolic fixed points. Cantor sets as hyperbolic repelling sets. Sequence spaces as metric spaces. Symbolic dynamics and coding. Dynamical systems and fractals. Hausdorff measure and dimension. Iterated functions systems: existence of the attractor, relationship with dynamical systems. Topological transitivity, sensitive dependence on initial conditions, chaos/chaotic maps, structural stability, period three implies chaos. The Schwarzian derivative. Bifurcation theory. Period doubling.