Fractal Geometry and Chaotic Dynamics

This course might not be offered in 2024. Please contact admin.teaching.msi@anu.edu.au for advice if you need this course to graduate. This course introduces basic mathematical techniques of fractal geometry and dynamical systems, aimed towards understanding and modeling natural shapes and forms from leaves to coastlines. Basic topological and geometrical language to describe and model rough, ("fractal") objects is developed. Relationships between fractal geometry and discrete dynamical systems and chaotic dynamics are emphasized, including symbolic dynamics, stability of attractors, bifurcations and routes to chaos. The key ideas are introduced in an intuitive way. The key definitions and theorems are stated but few proofs of theorems are given. However, graduate students will have to attend additional lectures which will provide rigorous mathematical foundations and will be assessed separately from undergraduate students. In computer laboratory sessions students learn how the mathematical results can be applied in practice by running and modifying simple Python programs.