### Attractors and their stability.

Ergodic Theory and Dynamical Systems Seminar

6th February 2020, 2:00 pm – 3:00 pm

Fry Building, 2.04

In unfoldings of rank-one homoclinic tangencies, there exist codimension 2 laminations of maps with infinitely many sinks. The sinks move simultaneously along the leaves. Similarly, there are codimension 2 laminations of maps with 2 period doubling Cantor attractors. A natural question to ask is whether strange attractors also exhibit this form of stability: do they occur in codimension 2 laminations? As first step in replaying to this question I will discuss the existence of codimension 2 laminations of maps with an invariant Cantor set having positive Lyapunov exponent. We obtain these invariant Cantor sets following the main steps of the construction of strange attractors by Benedicks and Carleson. In particular these Cantor sets have a critical point satisfying the Collet-Eckmann condition.

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