Abstract:

Planar vector fields $X$ near a saddle type $p:-q$ resonant singular point are considered. The use of Ecalle-Roussarie log-like compensators in linearizing conjugacies is carried out, and Gevrey-type estimates are presented. Attention is given to the unfolding of the resonance with one parameter.

In the analytic case an approximative normal form with a flat remainder of an explicit type is described, including parameter dependence, also in the (formally linearizable) non-resonant case.

Finally, we indicate some questions in the non-resonant case, about the possible use of compensators related to the rational approximants.

Slides of the talk part 1.

Slides of the talk part 2.

Video of the talk.