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Book Review
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Book Information
Author(s):
Colin Christopher and Chengzhi Li
Title:
Limit cycles of differential equations
Additional book information:
Advanced Courses in Mathematics, CRM Barcelona,
Birkhäuser Verlag, Basel,
2007,
viii+171 pp.,
ISBN 978-3-7643-8409-8
References:
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- [BNY]
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th problem, ArXiv preprint 0808-2952 (2008), 1-57. - [CD]
- M. Caubergh and F. Dumortier, Hilbert's
th problem for classical Liénard equations of even degree, J. Differential Equations 244 (2008), no. 6, 1359-1394. MR 2396502 - [Dul]
- H. Dulac, Sur les cycles limites, Bull. Soc. Math. France 51 (1923), 45-188. MR 1504823
- [D]
- F. Dumortier, Compactification and desingularization of spaces of polynomial Liénard equations, J. Differential Equations 224 (2006), no. 2, 296-313. MR 2223719
- [DF]
- F. Dumortier and P. Fiddelaers, Quadratic models for generic local
-parameter bifurcations on the plane, Trans. Amer. Math. Soc. 326 (1991), no. 1, 101-126. MR 1049864 - [DL]
- F. Dumortier and C. Li, Quadratic Liénard equations with quadratic damping, J. Differential Equations 139 (1997), no. 1, 41-59. MR 1467352
- [DLA]
- F. Dumortier, J. Llibre, and J. C. Artés, Qualitative theory of planar differential systems, Universitext. Springer-Verlag, Berlin, 2006. xvi+298 pp., ISBN: 3-540-32893-9 MR 2256001
- [DPR]
- F. Dumortier, D. Panazzolo, and R. Roussarie, More limit cycles than expected in Liénard equations, Proc. Amer. Math. Soc. 135 (2007), 1895-1904. MR 2286102
- [DR]
- F. Dumortier and R. Roussarie, Abelian integrals and limit cycles, J. Differential Equations 227 (2006), 116-165. MR 2233957
- [DRR]
- F. Dumortier, R. Roussarie, and C. Rousseau, Hilbert's
th problem for quadratic vector fields, J. Differential Equations 110 (1994), 86-133. MR 1275749 - [E]
- J. Écalle, Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac, Actualitiées Math., Hermann, Paris, 1992. MR 1399559
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- D. Hilbert, Mathematical problems, Bull. Amer. Math. Soc. 8 (1902), 437-479; reprinted, Bull. Amer. Math. Soc. (N.S.) 37 (2000), 407-436. MR 1779412
- [I1]
- Yu. Ilyashenko, Finiteness theorems for limit cycles, American Mathematical Society, Providence, RI, 1991. MR 1133882
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- Yu. Ilyashenko, Centennial history of Hilbert's
th problem, Bull. Amer. Math. Soc. (N.S.) 39 (2002), 301-354. MR 1898209 - [IP]
- Yu. Ilyashenko and A. Panov, Some upper estimates of the number of limit cycles of planar vector fields with applications to the Liénard equation, Mosc. Math. J. 1 (2001), no. 4, 583-599, 645. MR 1901077
- [LMP]
- A. Lins, W. De Melo, and C. C. Pugh, On Liénard's equation, Lectures Notes in Math. 597 (1977), 335-357. MR 0448423
- [LR]
- J. Llibre and G. Rodríguez, Configurations of limit cycles and planar polynomial vector fields, J. Differential Equations 198 (2004), no. 2, 374-380. MR 2039147
- [R1]
- R. Roussarie, Bifurcation of planar vector fields and Hilbert's
th problem, Progress in Mathematics, Vol. 164, Birkhauser Verlag, Basel, 1998. MR 1628014 - [R2]
- R. Roussarie, Putting a boundary to the space of Liénard equations, Discrete Contin. Dyn. Syst. 17 (2007), no. 2, 441-448. MR 2257444
- [RS]
- V. G. Romanovski and D. S. Shafer, The center and cyclicity problems, a computational algebra approach, Birkhäuser, Boston, Basel, Berlin, 2008, ISBN 978-0-8176-4726-1.
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- S. Shi, A concrete example of a quadratic system of the existence of four limit cycles for plane quadratic systems, Sci. Sinica 11 (1979), 1051-1056 (Chinese); 23 (1980), 153-158 (English). MR 0574405
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Additional Information:
Reviewer(s):
Freddy
Dumortier
Affiliation:
Hasselt University
Email:
freddy.dumortier@uhasselt.be
Review Information:
Journal:
Bull. Amer. Math. Soc.
46
(2009),
697-701.
MSC
(2000):
Primary 34C05, 34C07
DOI:
10.1090/S0273-0979-09-01267-1
PII:
S 0273-0979(09)01267-1
Posted:
June 24, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
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