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