Logic Seminar
Patrick Speissegger
McMaster University
O-minimality and correspondence maps of polycycles with hyperbolic singularities
Abstract: I start by outlining one of the strategies used to establish the o-minimality of certain expansions of the
real field. Working with Tobias Kaiser and Jean-Philippe Rolin, we are now trying to use apply this strategy
to the correspondence maps of polycycles of planar analytic vector fields, in the case where all the
singularities along the polycycle are hyperbolic. It turns out, based on Dulac's and Ilyashenko's work, that
if one assumes in addition that these hyperbolic singularities are all non-resonant, then a direct
application of one of the established techniques works. I will explain this result and speculate on its
possible extension to the general hyperbolic case.
Tuesday October 10, 2006 at 4:00 PM in SEO 427