Planar nonautonomous polynomial equations II. Coinciding sectors
type: Item
instance of: scholarly article
title: Planar nonautonomous polynomial equations II. Coinciding sectors
zbMATH Open document ID: 1170.34028
author: Paweł Wilczyński
published in: Journal of Differential Equations
publication date: 2009-04-29T00:00:00Z
review text: The paper presents some sufficient conditions for the existence of periodic solutions and heteroclinic connections of the equation \[ \dot z=\sum_{j=0}^na_j(t)z^j \] on the complex plane, where \(a_j\) are \(T\)-periodic continuous functions. It is a continuation of the previous research of the author published in the paper: ``Planar nonautonomous polynomial equations: the Riccati equation'' [J. Differ. Equations 244, No.~6, 1304--1328 (2008; Zbl 1147.34035)].
reviewed by: Roman Srzednicki
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 5549453
zbMATH Keywords: periodic solution
zbMATH Keywords: isolating segment
zbMATH Keywords: asymptotic stability
MaRDI profile type: Publication
full work available at URL: j.jde.2008.11.009
OpenAlex ID: W2016459592
cites work: A new uniqueness criterion for the number of periodic orbits of Abel equations
cites work: Periodic solutions of a quartic differential equation and Groebner bases
cites work: Periodic solutions of Abel differential equations
cites work: Non-autonomous equations related to polynomial two-dimensional systems
cites work: Periodic solutions of a quartic nonautonomous equation
cites work: Multiplicity of periodic solutions for the planar polynomial equation
cites work: Positive oriented periodic solutions of the first-order complex ODE with polynomial nonlinear part
cites work: Nonexistence of periodic solutions of a complex Riccati equation
cites work: Complex dynamics
cites work: Periodic orbits in complex Abel equations
cites work: Word problems related to derivatives of the displacement map
cites work: Periodic solutions of polynomial non-autonomous differential equations
cites work: Cyclicity of a critical point and the inverse Poincaré map
cites work: Cubic systems and Abel equations
cites work: Lectures on algebraic topology.
cites work: Q4226086
cites work: LIMIT CYCLES FOR GENERALIZED ABEL EQUATIONS
cites work: Limit Cycles for a Class of Abel Equations
cites work: Hilbert-type numbers for Abel equations, growth and zeros of holomorphic functions
cites work: On the number of solutions of the equation \(\sum^n_{j=0}a_j(t)x^j,0\leq t\leq 1\), for which \(x(0)=x(1)\)
cites work: The Number of Periodic Solutions of the Equation Ż=z N +p 1 (t )z
cites work: An equation \(\dot z=z^ 2+p(t)\) with no \(2\pi\)-periodic solutions
cites work: The number of periodic solutions of polynomial differential equations
cites work: On the diversity of Poincaré mappings for cubic equations with variable coefficients
cites work: Q5529795
cites work: Periodic solutions of polynomial first order differential equations
cites work: Composition operators and classical function theory
cites work: On periodic solutions of planar polynomial differential equations with periodic coefficients
cites work: Q5703735
cites work: A geometric method for detecting chaotic dynamics
cites work: Q3594199
cites work: Planar nonautonomous polynomial equations: the Riccati equation
cites work: The method of holomorphic foliations in planar periodic systems: The case of Riccati equations
cites work: Periodic planar systems without periodic solutions
DOI: 10.1016/J.JDE.2008.11.009
description: scientific article; zbMATH DE number 5549453