Polynomial differential systems with explicit non-algebraic limit cycles

Up to know all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have degree ≥ 5. Here we show that already there are polynomial differential systems of degree ≥ 3 exhibiting explicit non-algebraic limit cycles. It is well known that polynomial...

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Bibliographic Details
Authors: Benterki, Rebiha|||0000-0001-6745-2747, Llibre, Jaume|||0000-0002-9511-5999
Format: article
Publication Date:2012
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:150529
Online Access:https://ddd.uab.cat/record/150529
Access Level:Open access
Keyword:Non-algebraic limit cycle
Polynomial vector field
Description
Summary:Up to know all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have degree ≥ 5. Here we show that already there are polynomial differential systems of degree ≥ 3 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.