School of Mathematics and Statistics

Hyperbolic dynamics, zeta functions and fractals


Prof Luchezar Stoyanov
Telephone (+61 8) 6488 3393


This will be an introduction into the mathematical study of some kind of fractals. These are defined by the so-called Iterated Function Systems (IFS).  The lectures will begin with some basic information about metric spaces and the fixed point theorem for contraction maps.  We will then define IFS and study some general properties and some interesting examples.

Hyperbolic dynamical systems appear naturally in many areas of science and engineering. They usually exhibit strong chaotic properties and their maximal invariant sets often have a rather complicated (fractal) structure.

For example, to the right the figure is shown of the limit set of a reflection group acting on the hyperbolic 3D space (which generates a hyperbolic flow on an invariant set with a similar fractal structure).

Additional information about fractals and classic iterated function systems is available for you.

There will be three mini-classes 45 minutes in duration given at 1pm on Tuesdays in the Blakers Lecture Theatre.  No registration is required, simply turn up to your preferred class listed below. 



Hyperbolic dynamics, zeta functions and fractals : Prof Luchezar Stoyanov
Prof Luchezar Stoyanov

bout the lecturer:  Luchezar is a pure mathematician with interests in analysis, geometry and topology.


Week Dates Lecturer Topic
5, 6, 7 25 August, 1, 8 September Prof Luchezar Stoyanov Hyperbolic dynamics, zeta functions and fractals

Lecture notes

IFS1.pdf [PDF, 150.2 KB]
Updated 27 Aug 2015

IFS2.pdf [PDF, 479.9 KB]
Updated 1 Sep 2015

IFS3.pdf [PDF, 1.7 MB]
Updated 8 Sep 2015


School of Mathematics and Statistics

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Last updated:
Thursday, 1 October, 2015 4:04 PM