Selim Ghazouani

Generic dynamics and affine structures on surfaces

In this talk I will discuss the question that motivated the birth of dynamical systems as a subfield of maths: what does your typical dynamical system qualitatively looks like? I will start with historical considerations, from Poincaré and the question of the stability of the solar system to Smale’s conjecture about the density of hyperbolicity.

I will then specify these rather abstract considerations to very concrete families of dynamical systems. These are derived from geometric objects called affine structures on surfaces. If time permits, I will outline a conjectural programme about the dynamical properties of these surfaces and explain its consequences for the geometric aspects of the topic.