# Moscow Mathematical Journal

Volume 15, Issue 1, January–March 2015 pp. 141–178.

The Complete Formal Normal Form for the Bogdanov–Takens Singularity

**Authors**:
Ewa Stróżyna (1) and Henryk Żołądek (2)

**Author institution:**(1) Faculty of Mathematics and Information Sciences, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland

(2) Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland

**Summary: **

We solve completely the problem of formal classification of
the vector fields of the form *x˙* = *y* + ..., *y˙* = ... using formal changes of
the coordinates but not of the time. In the proofs we avoid complicated
calculations. The method we use is effective and can be applied in other
classification problems.

2010 Math. Subj. Class. Primary: 05C38, 15A15; Secondary: 05A15, 15A18.

**Keywords: **Nilpotent singularity, formal orbital normal form, non-orbital normal form.

Contents
Full-Text PDF