A system of degree four with an invariant triangle and at least three small amplitude limit cycles

A system of degree four with an invariant triangle and at least three small amplitude limit cycles

We show the existence of a polynomial system of degree four having three real invariant straight lines forming a triangle with at least three small amplitude limit cycles in the interior. Also, we obtain the necessary and sufficient conditions for the critical point at the interior of the bounded...

Full description

Bibliographic Details
Main Authors: Zhenhai Liu, E. Sáez, I. Szántó
Format: Article
Language:English
Published: University of Szeged 2010-11-01
Series:Electronic Journal of Qualitative Theory of Differential Equations
Online Access:http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=529
id doaj-c446ce87f43e4b329fc5a79165882aa1
record_format Article
spelling doaj-c446ce87f43e4b329fc5a79165882aa12021-07-14T07:21:22ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751417-38752010-11-012010691710.14232/ejqtde.2010.1.69529A system of degree four with an invariant triangle and at least three small amplitude limit cyclesZhenhai Liu0E. Sáez1I. Szántó2Guangxi University for Nationalities, Nanning, Guangxi, P. R. ChinaUniversidad Tecnica Federico Santa Maria, Valparaiso, ChileUniversidad Tecnica Federico Santa Maria, Valparaiso, ChileWe show the existence of a polynomial system of degree four having three real invariant straight lines forming a triangle with at least three small amplitude limit cycles in the interior. Also, we obtain the necessary and sufficient conditions for the critical point at the interior of the bounded region to be a center.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=529
collection DOAJ
language English
format Article
sources DOAJ
author Zhenhai Liu
E. Sáez
I. Szántó
spellingShingle Zhenhai Liu
E. Sáez
I. Szántó
A system of degree four with an invariant triangle and at least three small amplitude limit cycles
Electronic Journal of Qualitative Theory of Differential Equations
author_facet Zhenhai Liu
E. Sáez
I. Szántó
author_sort Zhenhai Liu
title A system of degree four with an invariant triangle and at least three small amplitude limit cycles
title_short A system of degree four with an invariant triangle and at least three small amplitude limit cycles
title_full A system of degree four with an invariant triangle and at least three small amplitude limit cycles
title_fullStr A system of degree four with an invariant triangle and at least three small amplitude limit cycles
title_full_unstemmed A system of degree four with an invariant triangle and at least three small amplitude limit cycles
title_sort system of degree four with an invariant triangle and at least three small amplitude limit cycles
publisher University of Szeged
series Electronic Journal of Qualitative Theory of Differential Equations
issn 1417-3875
1417-3875
publishDate 2010-11-01
description We show the existence of a polynomial system of degree four having three real invariant straight lines forming a triangle with at least three small amplitude limit cycles in the interior. Also, we obtain the necessary and sufficient conditions for the critical point at the interior of the bounded region to be a center.
url http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=529
work_keys_str_mv AT zhenhailiu asystemofdegreefourwithaninvarianttriangleandatleastthreesmallamplitudelimitcycles
AT esaez asystemofdegreefourwithaninvarianttriangleandatleastthreesmallamplitudelimitcycles
AT iszanto asystemofdegreefourwithaninvarianttriangleandatleastthreesmallamplitudelimitcycles
AT zhenhailiu systemofdegreefourwithaninvarianttriangleandatleastthreesmallamplitudelimitcycles
AT esaez systemofdegreefourwithaninvarianttriangleandatleastthreesmallamplitudelimitcycles
AT iszanto systemofdegreefourwithaninvarianttriangleandatleastthreesmallamplitudelimitcycles
_version_ 1721303749180260352

Similar Items