The Kate Edger Department of Mathematics


The geometry of chaos

appliedmathematicswild

 

The notion of chaotic dynamics has been popularised enormously with the famous butterfly attractor of the Lorenz system. Mathematically, we are interested in how such chaotic dynamics develops as parameters vary in a dynamical system. At The University of Auckland we take a geometric point of view and use advanced numerical tools to understand changes in the topological nature of invariant manifolds. These ideas bring together different fields from pure and applied mathematics and offer the opportunity for exciting new insights.

Our interest is not only in `classical chaos´ as for the Lorenz system, but also in `wild chaos´ that can only occur in higher-dimensional systems. Wild chaos can be studied using reductions to a two-dimensional non-invertible map. Our goal is to understand different types of chaos and how they differ from classical chaos.

         Figure taken from: SIAM Journal on Applied Dynamical Systems 12: 1280-1329 (2013)

 

 

Researchers at The University of Auckland

 

Other Collaborators