Computing center conditions for vector fields with constant angular speed

We investigate the planar analytic systems which have a center-focus equilibrium at the origin and whose angular speed is constant. The conditions for the origin to be a center (in fact, an isochronous center) are obtained. Concretely, we find conditions for the existence of a Cw-commutator of the f...

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Bibliographic Details
Authors: Algaba Durán, Antonio, Reyes Columé, Manuel
Format: article
Publication Date:2003
Country:España
Institution:Universidad de Huelva (UHU)
Repository:Arias Montano. Repositorio Institucional de la Universidad de Huelva
Language:English
OAI Identifier:oai:ariasmontano.uhu.es:10272/25437
Online Access:https://hdl.handle.net/10272/25437
Access Level:Open access
Keyword:Limit cycles
Periodic solutions
1206.02 Ecuaciones Diferenciales
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spelling Computing center conditions for vector fields with constant angular speedAlgaba Durán, AntonioReyes Columé, ManuelLimit cyclesPeriodic solutions1206.02 Ecuaciones DiferencialesWe investigate the planar analytic systems which have a center-focus equilibrium at the origin and whose angular speed is constant. The conditions for the origin to be a center (in fact, an isochronous center) are obtained. Concretely, we find conditions for the existence of a Cw-commutator of the field. We cite several subfamilies of centers and obtain the centers of the cuartic polynomial systems and of the families (-y + x(H1 + Hm), x + y(H1 + Hm)1 and (-y + x(H2 + H2n), x + y(H2 + H2n))t, with H i homogeneous polynomial in x,y of degree i. In these cases, the maximum number of limit cycles which can bifurcate from a fine focus is determined.Elsevier20032003-05-0120032003-05-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10272/25437reponame:Arias Montano. Repositorio Institucional de la Universidad de Huelvainstname:Universidad de Huelva (UHU)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Atribución-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nd/3.0/es/info:eu-repo/semantics/openAccessoai:ariasmontano.uhu.es:10272/254372026-06-02T14:58:11Z
dc.title.none.fl_str_mv Computing center conditions for vector fields with constant angular speed
title Computing center conditions for vector fields with constant angular speed
spellingShingle Computing center conditions for vector fields with constant angular speed
Algaba Durán, Antonio
Limit cycles
Periodic solutions
1206.02 Ecuaciones Diferenciales
title_short Computing center conditions for vector fields with constant angular speed
title_full Computing center conditions for vector fields with constant angular speed
title_fullStr Computing center conditions for vector fields with constant angular speed
title_full_unstemmed Computing center conditions for vector fields with constant angular speed
title_sort Computing center conditions for vector fields with constant angular speed
dc.creator.none.fl_str_mv Algaba Durán, Antonio
Reyes Columé, Manuel
author Algaba Durán, Antonio
author_facet Algaba Durán, Antonio
Reyes Columé, Manuel
author_role author
author2 Reyes Columé, Manuel
author2_role author
dc.contributor.none.fl_str_mv
dc.subject.none.fl_str_mv Limit cycles
Periodic solutions
1206.02 Ecuaciones Diferenciales
topic Limit cycles
Periodic solutions
1206.02 Ecuaciones Diferenciales
description We investigate the planar analytic systems which have a center-focus equilibrium at the origin and whose angular speed is constant. The conditions for the origin to be a center (in fact, an isochronous center) are obtained. Concretely, we find conditions for the existence of a Cw-commutator of the field. We cite several subfamilies of centers and obtain the centers of the cuartic polynomial systems and of the families (-y + x(H1 + Hm), x + y(H1 + Hm)1 and (-y + x(H2 + H2n), x + y(H2 + H2n))t, with H i homogeneous polynomial in x,y of degree i. In these cases, the maximum number of limit cycles which can bifurcate from a fine focus is determined.
publishDate 2003
dc.date.none.fl_str_mv 2003
2003-05-01
2003
2003-05-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10272/25437
url https://hdl.handle.net/10272/25437
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución-SinDerivadas 3.0 España
http://creativecommons.org/licenses/by-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución-SinDerivadas 3.0 España
http://creativecommons.org/licenses/by-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Arias Montano. Repositorio Institucional de la Universidad de Huelva
instname:Universidad de Huelva (UHU)
instname_str Universidad de Huelva (UHU)
reponame_str Arias Montano. Repositorio Institucional de la Universidad de Huelva
collection Arias Montano. Repositorio Institucional de la Universidad de Huelva
repository.name.fl_str_mv
repository.mail.fl_str_mv
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