J. Llibre, “Open problems on the algebraic limit cycles of planar polynomial vector fields”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2008, no. 1, 19

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica

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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2008, Number 1, Pages 19–26 (Mi basm2)

This article is cited in 11 scientific papers (total in 11 papers)

Open problems on the algebraic limit cycles of planar polynomial vector fields

J. Llibre

Departament de Matemàtiques, Universitat Autònoma de Barcelona

Full-text PDF (123 kB) Citations (11)

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Abstract: We collect several open problems that have appeared in the study of the algebraic limit cycles of the real planar polynomial vector fields.

Keywords and phrases: Algebraic limit cycle, polynomial vector field, Poincaré problem, invariant algebraic curve.

Received: 05.12.2007

Bibliographic databases:

MSC: 34C05

Language: English

Citation: J. Llibre, “Open problems on the algebraic limit cycles of planar polynomial vector fields”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2008, no. 1, 19–26

Citation in format AMSBIB

\Bibitem{Lli08}

\by J.~Llibre

\paper Open problems on the algebraic limit cycles of planar polynomial vector fields

\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.

\yr 2008

\issue 1

\pages 19--26

\mathnet{http://mi.mathnet.ru/basm2}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2392677}

\zmath{https://zbmath.org/?q=an:05375353}

Linking options:

https://www.mathnet.ru/eng/basm2

https://www.mathnet.ru/eng/basm/y2008/i1/p19

This publication is cited in the following 11 articles:

Li T. Llibre J., “Phase Portraits of Separable Quadratic Systems and a Bibliographical Survey on Quadratic Systems”, Expo. Math., 39:4 (2021), 540–565
Llibre J., Zhang X., “A Survey on Algebraic and Explicit Non-Algebraic Limit Cycles in Planar Differential Systems”, Expo. Math., 39:1 (2021), 48–61
Llibre J., Valls C., “Algebraic Limit Cycles on Quadratic Polynomial Differential Systems”, Proc. Edinb. Math. Soc., 61:2 (2018), 499–512
Buzzi C.A., Gasull A., Torregrosa J., “Algebraic Limit Cycles in Piecewise Linear Differential Systems”, Int. J. Bifurcation Chaos, 28:3 (2018), 1850039
Zegeling A., Kooij R.E., “Quadratic Systems With a Symmetrical Solution”, Electron. J. Qual. Theory Differ., 2018, no. 32, 1–18
Llibre J., Valls C., “On the Uniqueness of Algebraic Limit Cycles For Quadratic Polynomial Differential Systems With Two Pairs of Equilibrium Points At Infinity”, Geod. Dedic., 191:1 (2017), 37–52
Zhang X., “Integrability of Dynamical Systems: Algebra and Analysis”, Integrability of Dynamical Systems: Algebra and Analysis, Developments in Mathematics, 47, Springer, 2017, 1–380
Llibre J., Ramirez R., “Inverse Problems in Ordinary Differential Equations and Applications”, Inverse Problems in Ordinary Differential Equations and Applications, Progress in Mathematics, 313, Birkhauser Verlag Ag, 2016, 1–266
Llibre J., Schlomiuk D., “on the Limit Cycles Bifurcating From An Ellipse of a Quadratic Center”, Discret. Contin. Dyn. Syst., 35:3 (2015), 1091–1102
Yu Xiaolan, Zhang Xiang, “The hyperelliptic limit cycles of the Liénard systems”, J. Math. Anal. Appl., 376:2 (2011), 535–539
Llibre J., Ramírez R., Sadovskaia N., “On the 16th Hilbert problem for algebraic limit cycles”, J. Differential Equations, 248:6 (2010), 1401–1409

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica

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Full-text PDF :	217
References:	101
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