A topological perturbation theorem for infinite dimensional systems

Friday, September 28, 2012 - 9:00am - 9:50am
Keller 3-180
Konstantin Mischaikow (Rutgers, The State University Of New Jersey )
Conley theory has proven to be a useful tool for the analysis of global dynamics.
Its power arises from the fact that the index provides information about the existence
and structure of dynamics, but remains constant as long as isolation is preserved.
In particular, it allows one to compute or model the dynamics using one - preferably
simple to understand - system and draw conclusions about the dynamics of other systems.

The motivation for the work discussed is that there are a variety of problems which arise in study of
the dynamics of PDEs for which the natural phase space of the known system is
different from the natural phase space of the system of interest. Attempting to
apply Conley theory in this setting immediately leads to two problems:
(1) one needs to be able to deduce isolation in one phase space from different phase space, and
(2) one needs to be able to argue efficiently that the Conley index remains unchanged.
I will discuss an approach to dealing with these two problems.

This is joint work with G. Raugel.
MSC Code: