Normal forms of analytic vector fields

Laurent Stolovitch
Université de Nice, France
17th June 2013 14:00-15:00, Carslaw Room 829 (AGR)

Abstract

I will talk about local classification of germs of holomorphic vector fields vanishing at zero. It is always possible to transform, by a formal change of coordinates, a vector field into a simpler model, called a normal form. Such a transformation is usually a divergent formal power series at the origin. I will show how the problem of convergence is related to a small divisors condition. If the convergence cannot be obtained, I’ll show that the conjugacy can be Gevrey smooth or holomophic in a sectorial domain which contains zero in the boundary in some cases.

Check also the PDE Seminar page. Enquiries to Florica Cîrstea or Daniel Daners.