Periodic orbits for perturbed non-autonomous differential equations
type: Item
instance of: scholarly article
title: Periodic orbits for perturbed non-autonomous differential equations
zbMATH Open document ID: 1268.34072
author: Armengol Gasull
author: B. Coll
author: Rafel Prohens
published in: Bulletin des Sciences Mathématiques
publication date: 2012-10-26T00:00:00Z
review text: The paper deals with non-autonomous differential equations on the cylinder \((t,r)\in \mathcal S^{1}\times \mathbb R^{d}\) which can be written as \[ dr/dt=f(t,r,\varepsilon ). \] Under the assumption that the corresponding unperturbed equation (\(\varepsilon =0\)) has an open continuum of periodic solutions, the authors study the variational equations of low order. The derived results are applied to several families of differential equations with \(d=1,2,3\) including some autonomous polynomial differential equations as well as some non-autonomous Abel differential equations.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37C27
Mathematics Subject Classification ID: 37C60
zbMATH DE Number: 6099116
zbMATH Keywords: bifurcation
zbMATH Keywords: periodic orbit
zbMATH Keywords: limit cycle
zbMATH Keywords: variational equation
zbMATH Keywords: Abel equation
MaRDI profile type: Publication
full work available at URL: j.bulsci.2012.03.001
OpenAlex ID: W2053819109
cites work: Q5462937
cites work: Q5421220
cites work: Periodic solutions of nonlinear periodic differential systems with a small parameter
cites work: Q5472808
cites work: Limit cycles of differential equations
cites work: Polynomial systems: a lower bound for the Hilbert numbers
cites work: Periodic orbits in complex Abel equations
cites work: Limit cycles of some polynomial differential systems in dimension 2, 3 and 4, via averaging theory
cites work: Q3139838
cites work: HYPERBOLIC PERIODIC ORBITS FROM THE BIFURCATION OF A FOUR-DIMENSIONAL NONLINEAR CENTER
cites work: LIMIT CYCLES FOR GENERALIZED ABEL EQUATIONS
cites work: A new approach to the computation of the Lyapunov constants
cites work: Hilbert-type numbers for Abel equations, growth and zeros of holomorphic functions
cites work: Linear estimate for the number of zeros of Abelian integrals for quadratic isochronous centres
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: Limit cycles of polynomial differential systems bifurcating from the periodic orbits of a linear differential system in \(\mathbb R^d\)
cites work: Limit cycles for generalized Kukles polynomial differential systems
cites work: Limit cycles of the generalized polynomial Liénard differential equations
cites work: On a Class of Differential Equations of Riccati Type
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
DOI: 10.1016/J.BULSCI.2012.03.001
description: scientific article; zbMATH DE number 6099116