On nonexistence of algebraic curve solutions to second-order polynomial autonomous systems over the complex field.
type: Item
instance of: scholarly article
title: On nonexistence of algebraic curve solutions to second-order polynomial autonomous systems over the complex field.
zbMATH Open document ID: 1094.34513
author: Zhaosheng Feng
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2003-09-25T00:00:00Z
review text: Consider the polynomial system \[ \frac{dx}{dt}=y,\quad \frac{dy} {dt}=y \sum^\ell_{i=1}c_ix^i+\sum^\ell_{i=1}g_ix^i\tag{*} \] with \(c_i,g_i\in\mathbb{C}\), \(c_\ell g_\ell\neq 0\). The author proves that (*) has no solution of the form \[ \sum^m_{i=0}a_i(x)y^i=0, \] where \(a_i\) are polynomials in \(x\).
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C08
zbMATH DE Number: 1921204
MaRDI profile type: Publication
full work available at URL: s102550200068
OpenAlex ID: W2016784272
cites work: The Burgers equation under deterministic and stochastic forcing
cites work: Q4157021
cites work: Q4528360
cites work: Q1907159
cites work: Complex linear groups of degree less than \(4p/3\)
cites work: Q5183880
DOI: 10.1007/S102550200068
description: scientific article; zbMATH DE number 1921204