Translator Disclaimer
march 2019 Gevrey series in compensators linearizing a planar resonant vector field and its unfolding
Patrick Bonckaert
Bull. Belg. Math. Soc. Simon Stevin 26(1): 21-62 (march 2019). DOI: 10.36045/bbms/1553047227

Abstract

We consider a planar vector field $X$ near a saddle type $p:-q$ resonant singular point. Assuming that it has a normal form with a Gevrey-$d$ expansion (like $d=p+q$ which is in particular the case when starting from an analytic vector field) we show that $X$ can be linearized working with a change of coordinates that is of Gevrey order $d$ in certain $\log$-like variables, called compensators or also tags, multiplied by the first integral $u=x^qy^p$ of the linear part. Next we consider the unfolding of such a resonance, and provide (weaker) Gevrey-type linearization using compensators.

Citation

Download Citation

Patrick Bonckaert. "Gevrey series in compensators linearizing a planar resonant vector field and its unfolding." Bull. Belg. Math. Soc. Simon Stevin 26 (1) 21 - 62, march 2019. https://doi.org/10.36045/bbms/1553047227

Information

Published: march 2019
First available in Project Euclid: 20 March 2019

zbMATH: 07060314
MathSciNet: MR3934079
Digital Object Identifier: 10.36045/bbms/1553047227

Rights: Copyright © 2019 The Belgian Mathematical Society

JOURNAL ARTICLE
42 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.26 • No. 1 • march 2019
Back to Top