Sébastien Biebler: Blenders and almost blenders

Abstract:

A blender is a hyperbolic basic set with very special fractal properties: its unstable set intersects robustly any perturbation of a submanifold of dimension lower than its stable dimension. Introduced by Bonatti and Díaz in the 90s, blenders turned out to have many powerful applications to differentiable dynamics: construction of robustly transitive nonhyperbolic diffeomorphisms, density of stable ergodicity, Newhouse phenomenon, the existence of generic families displaying robustly infinitely many sinks, robust bifurcations in complex dynamics, fast growth of the number of periodic points… In this talk, I will survey how to construct blenders and use them to solve some of these questions. Then I will introduce a recent generalization from a measurable point of view, called almost blenders.