Limit cycles and invariant cylinders for a class of continuous and discontinuous vector field in dimention \(2n\)
type: Item
instance of: scholarly article
title: Limit cycles and invariant cylinders for a class of continuous and discontinuous vector field in dimention \(2n\)
zbMATH Open document ID: 1242.34069
author: Jaume Llibre
author: Maurício Firmino Silva Lima
published in: Applied Mathematics and Computation
publication date: 2011-07-22T00:00:00Z
review text: The paper deals with the bifurcation of limit cycles and invariant cylinders from a global center of a linear differential system in dimension \(2n\) perturbed inside the class of continuous or discontinuous piecewise linear vector fields represented by \[ \dot{x}=A_0x+\varepsilon F(x). \] The main results state the existence of at most one limit cycle and of at most one invariant cylinder. For the proof the authors use the expansion of the displacement function up to first order with respect to the small parameter and apply the averaging theory in a form that allows to avoid the differentiability of the system.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C45
zbMATH DE Number: 5931352
zbMATH Keywords: equilibrium point
zbMATH Keywords: periodic orbit
zbMATH Keywords: limit cycle
zbMATH Keywords: invariant cylinder
zbMATH Keywords: continuous piecewise linear vector field
zbMATH Keywords: discontinuous piecewise linear vector field
MaRDI profile type: Publication
full work available at URL: j.amc.2011.04.069
OpenAlex ID: W1988468789
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DOI: 10.1016/J.AMC.2011.04.069
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description: scientific article; zbMATH DE number 5931352