## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**Title:** Normally Hyperbolic foliations by circles

**Speaker:** Pablo Carrasco

**Speaker Info:** University of Toronto

**Brief Description:**

**Special Note**:

**Abstract:**

A continuous flow is said to be periodic (or compact) if all its
trajectories are closed. For a periodic flow in a compact manifold a
basic question is whether there exist a uniformly upper bound in the
periods of the orbits; the existence of this bound ties firmly the
geometry of the orbit foliation (meaning, the foliation given by the
orbits of the flow) with the transverse structure and allows nice
local models for the neighborhoods of the orbits.
It was D. Sullivan who in 1976 found an striking counterexample of a
periodic flow in the five sphere where there is no upper bound for the
periods, and hence preventing the existence of these nice local
models.
But now suppose that you have a periodic flow on a compact manifold
whose orbit foliation $\mathcal{F}$\ is normally hyperbolic. Can you
say something about the geometry of this foliation, and in particular,
is there a uniform upper bound for the periods?
In this talk we'll try to answer this and related questions. As a
result we will also obtain information about the dynamics of the
normally hyperbolic map preserving $\mathcal{F}$.

**Date:** Tuesday, November 02, 2010

**Time:** 3:00pm

**Where:** Lunt 105

**Contact Person:** Prof. Ana Rechtman

**Contact email:** rechtman@math.northwestern.edu

**Contact Phone:**

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