Polynomial differential systems with explicit non-algebraic limit cycles

Up to now all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have degree at most 5. Here we show that already there are polynomial differential systems of degree at least exhibiting explicit non-algebraic limit cycles. It is well known t...

Full description

Bibliographic Details
Main Authors:	Rebiha Benterki, Jaume Llibre
Format:	Article
Language:	English
Published:	Texas State University 2012-05-01
Series:	Electronic Journal of Differential Equations
Subjects:	Non-algebraic limit cycle polynomial vector field
Online Access:	http://ejde.math.txstate.edu/Volumes/2012/78/abstr.html

id	doaj-77042f114c3b41728c4720acae40b15c
record_format	Article
spelling	doaj-77042f114c3b41728c4720acae40b15c2020-11-24T21:03:10ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-05-01201278,16Polynomial differential systems with explicit non-algebraic limit cyclesRebiha BenterkiJaume LlibreUp to now all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have degree at most 5. Here we show that already there are polynomial differential systems of degree at least exhibiting explicit non-algebraic limit cycles. It is well known that polynomial differential systems of degree 1 (i.e. linear differential systems) has no limit cycles. It remains the open question to determine if the polynomial differential systems of degree 2 can exhibit explicit non-algebraic limit cycles. http://ejde.math.txstate.edu/Volumes/2012/78/abstr.htmlNon-algebraic limit cyclepolynomial vector field
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Rebiha Benterki Jaume Llibre
spellingShingle	Rebiha Benterki Jaume Llibre Polynomial differential systems with explicit non-algebraic limit cycles Electronic Journal of Differential Equations Non-algebraic limit cycle polynomial vector field
author_facet	Rebiha Benterki Jaume Llibre
author_sort	Rebiha Benterki
title	Polynomial differential systems with explicit non-algebraic limit cycles
title_short	Polynomial differential systems with explicit non-algebraic limit cycles
title_full	Polynomial differential systems with explicit non-algebraic limit cycles
title_fullStr	Polynomial differential systems with explicit non-algebraic limit cycles
title_full_unstemmed	Polynomial differential systems with explicit non-algebraic limit cycles
title_sort	polynomial differential systems with explicit non-algebraic limit cycles
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2012-05-01
description	Up to now all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have degree at most 5. Here we show that already there are polynomial differential systems of degree at least exhibiting explicit non-algebraic limit cycles. It is well known that polynomial differential systems of degree 1 (i.e. linear differential systems) has no limit cycles. It remains the open question to determine if the polynomial differential systems of degree 2 can exhibit explicit non-algebraic limit cycles.
topic	Non-algebraic limit cycle polynomial vector field
url	http://ejde.math.txstate.edu/Volumes/2012/78/abstr.html
work_keys_str_mv	AT rebihabenterki polynomialdifferentialsystemswithexplicitnonalgebraiclimitcycles AT jaumellibre polynomialdifferentialsystemswithexplicitnonalgebraiclimitcycles
_version_	1716773947369848832

Polynomial differential systems with explicit non-algebraic limit cycles

Similar Items