Periodic orbits, Lyapunov Exponents and Recurrence

CCNY Dynamical Systems Seminar

Time and place

1 PM on Thursday, November 18th, 2010; NAC 6-113

Krerley Oliveira (UFAL)

Abstract

Periodic orbits are one main actor in dynamical systems. Despite the fact that in some setting they are extremely difficult to obtain, under a "sufficient chaotic" situation there are plenty of them. How they are distributed plays a important role in the study of dynamical systems.

In this talk we prove the following result: given a (ergodic) invariant measure for C1 a dynamical system with only positive Lyapunov exponents, we are able to show that almost every point is shadowed by a periodic orbit with period that growth sublinearly with the size of the piece of orbit that you wanna shadow. We discuss some interesting applications on recurrence estimates and approximations by periodic measures.

We do not assume any prior knowledge of dynamical systems and we gonna try to make a (as much as possible) self-contained presentation.