Geodesic
The problem of distinguishing between a~centre and a~focus in the space of vector fields with given Newton diagram
Sbornik. Mathematics, Tome 211 (2020) no. 10, pp. 1399-1446

Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate the problem of distinguishing between a centre and a focus in the class of analytic vector fields with fixed Newton diagram, which satisfy certain natural conditions of general position. A method is proposed for constructing explicit expressions for the coefficients in the asymptotic representation of the monodromy transformation, known as the Dulac series. These are analogous to the Lyapunov focal quantities. These coefficients make it possible — up to an infinite-codimensional set of exceptional cases — to complete the stability analysis for a compound monodromic (that is, centre-focus) singular point. A computer-aided calculation of formulae for coefficients of the Dulac series is presented. Examples are treated of Newton diagrams with two and three edges. Bibliography: 30 titles.
Keywords: Dulac series, Newton diagram
Mots-clés : monodromic singular point, monodromy transformation, transition map. 
@article{SM_2020_211_10_a2,
     author = {N. B. Medvedeva},
     title = {The problem of distinguishing between a~centre and a~focus in the space of vector fields with given {Newton} diagram},
     journal = {Sbornik. Mathematics},
     pages = {1399--1446},
     publisher = {mathdoc},
     volume = {211},
     number = {10},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2020_211_10_a2/}
}
TY  - JOUR
AU  - N. B. Medvedeva
TI  - The problem of distinguishing between a~centre and a~focus in the space of vector fields with given Newton diagram
JO  - Sbornik. Mathematics
PY  - 2020
SP  - 1399
EP  - 1446
VL  - 211
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2020_211_10_a2/
LA  - en
ID  - SM_2020_211_10_a2
ER  - 
%0 Journal Article
%A N. B. Medvedeva
%T The problem of distinguishing between a~centre and a~focus in the space of vector fields with given Newton diagram
%J Sbornik. Mathematics
%D 2020
%P 1399-1446
%V 211
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2020_211_10_a2/
%G en
%F SM_2020_211_10_a2
N. B. Medvedeva. The problem of distinguishing between a~centre and a~focus in the space of vector fields with given Newton diagram. Sbornik. Mathematics, Tome 211 (2020) no. 10, pp. 1399-1446. http://geodesic.mathdoc.fr/item/SM_2020_211_10_a2/