2008-2009

Mario Martelli

**Monday, February 9
Millikan 213
(Pomona College), 3:00 PM**

**Title: **Eliminating chaos

Abstract: We would like to achieve
three goals:

1. Give a simple definition of chaotic behavior for a self-map of a
compact metric space. Among the examples we will talk about the
Bernoulli shift on bilateral sequences of finitely many symbols (20
minutes).

2.Talk about the Poincaré approach and the theorem of S. Smale
on the transversal intersection of the stable and unstable manifold (20
minutes).

3. Present a recent theorem (no proof) of G. Di Lena, D. Franco, M.
Martelli, and B. Messano on the removal of chaos from certain dynamical
systems with the introduction of small perturbations (20 minutes).