TITLE:
Study of volume-preserving flows guided by the Michelson system

AUTHOR:
Ainoa Murillo
 Departament de Matematiques i Informatica
 Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain

E-mail: ainoa@maia.ub.es

ABSTRACT:
We consider three-dimensional volume-preserving flows and we study aspects of
its dynamics. We describe the geometry of flows having a volume-preserving
symmetry. Perturbations of such flows are reduced to Poincaré (not necessarily
canonical) area-preserving maps. We present a detailed study of the phase space
of area-preserving maps through Birkhoff normal form. These results are
illustrated by the Michelson system. Comments on the asymptotic behaviour of
the splitting of the invariant manifolds of this system are given. Finally, we
include a preliminary description of the dynamics of a discretization of the
Michelson flow. It shows richer dynamics than the flow that we try to show
through some numerical investigations.