Wednesday, February 16, 2011

On the Gap Lemma

Pedro Duarte

Abstract: The Gap Lemma is a one-dimensional technical tool in the theory of smooth dynamical systems. It is based on the concept of thickness of a Cantor set, that was introduced by Sheldon Newhouse to prove complex dynamical phenomena like wild hyperbolic sets, persistent homoclinic tangencies and coexistence of infinitely many sinks. We shall prove a generalisation of the Gap Lemma due to Gustavo Moreira and explain how distortion bounds are used to estimate thickness and prove its continuity.

Wednesday, February 16, 2011
Time: 15h00
Room: Sala 306, Edificio Quelhas, ISEG