Exceptional sets in parameter spaces of dynamical systems

Many dynamical systems arise naturally as parametrised families. One can then study the associated parameter space and ask how qualitative properties of the dynamics are reflected geometrically within it. In this talk I will discuss three examples where classification problems lead to intricate subsets of parameter space: the Mandelbrot set in complex dynamics, the Rauzy gasket arising from interval exchange transformations, and a tiling structure associated with the topological classification of a family of self-similar sets. Although these examples arise in very different settings, they exhibit striking parallels in how parameter spaces organise qualitative changes in the underlying dynamics.

Venue: Fulton G20