The leading term of the first return map of a singular point with a fixed Newton diagram
type: Item
instance of: scholarly article
title: The leading term of the first return map of a singular point with a fixed Newton diagram
zbMATH Open document ID: 0902.34027
author: N. B. Medvedeva
published in: Journal of Mathematical Sciences (New York)
publication date: 1998-08-17T00:00:00Z
review text: Analytic vector fields of dynamic systems \[ \begin{aligned} y\dot x & = X(x,y)= \sum a_{ij}x^i y^j,\\ x\dot y & = Y(x,y)= \sum b_{ij}x^i y^j,\quad (a_{ij}, b_{ij})\neq(0,0),\end{aligned} \] are considered. The coefficient of the leading term in the asymptotics of the Poincaré function of the vector fields with a fixed Newton diagram \(\Gamma\) is computed. The \(\Gamma\)-nondegenerate vector fields satisfying two conditions of nondegeneracy are investigated.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 1058642
zbMATH Keywords: dynamic systems
zbMATH Keywords: Poincaré function
zbMATH Keywords: Newton diagram
zbMATH Keywords: nondegeneracy
reviewed by: Izabela Foltyńska
MaRDI profile type: Publication
cites work: Principal term of the monodromy transformation of a monodromic singular point is linear
description: scientific article; zbMATH DE number 1058642