
DYNAMICAL SYSTEMS SEMINAR DAY
Thursday, November 7, 1996
PROGRAM:
Stephen Morris, University of Toronto
Experiments on Convection Patterns (Boardroom)
Robust Heteroclinic Cycles in Symmetric Systems
Martin Krupa, Technical University, Vienna
Robust Heteroclinic Cycles in Symmetric Systems

ABSTRACTS:
Stephen Morris: "Experiments on Convection Patterns"
Fluid convection makes a nice laboratoryscale system in which to
do precise studies of pattern formation under nonlinear, nonequilibrium
conditions. I will describe recent work on a couple of convection
experiments, RayleighBenard convection in gases and electrically
driven convection in smectic liquid crystals. In each case, the
system makes a transition to an ordered flow pattern, followed by
a second transition to a chaotic state.
Martin Krupa: "Robust Heteroclinic Cycles in Symmetric Systems"
Heteroclinic cycles do not normally persist in systems of differential
equations without symmetry. However, in symmetric systems, heteroclinic
cycles can be robust under symmetrypreserving perturbations, and
can also be stable in the Liapunov sense. Evidence of such cycles
has been observed in numerical simulations and physical experiments,
for example in rotating convection between two plates and turbulent
flows in a boundary layer. The existence of robust heteroclinic
cycles has been proven theoretically in the unfoldings of some low
codimension bifurcations and in forced symmetrybreaking from a
larger to a smaller symmetry group. This talk will review both theoretical
and applied research on robust heteroclinic cycles.

