Dense Orbits in Area Preservings flows on Surfaces
by
Michael D. Hirsch
Dept. of Math and CS, Emory University

Let F be a closed surface of genus g > 1. Let X be a smooth vector field on F inducing a flow \phi_t. A theorem due to Poincaré says that if \phi_t is area preserving, then almost every point of F is recurrent under \phi_t.

In this talk I will examine the \omega-limit sets of orbits, and prove in particular that if F has hyperbolic singularities, and \phi_t has no close orbits, then \phi_t must have a dense orbit.

Date received: February 26, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caam-24.