Unfolding of resonant saddles and the Dulac time
Speaker:
David Marín Pérez, Universitat Autònoma de Barcelona
Date and Time:
Wednesday, June 24, 2009 - 3:30pm to 4:30pm
Location:
Fields Institute, Room 230
Abstract:
In this work we study unfoldings of planar vector fields in a neighborhood of a resonant saddle. We give a C k temporal normal form for the unfolding. That is, a normal form with respect to the conjugacy relation. Using our temporal normal form we determine an asymptotic development, uniform with respect to the parameters, of the Dulac time of a resonant saddle. Conjugacy relation instead of weaker equivalence relation is necessary when studying the time function. The Dulac time of a resonant saddle can be seen as the basic building block of the total period function of an unfolding of a hyperbolic polycycle. (joint work with Pavao Mardesic and Jordi Villadelprat)