Hilbert’s 16th Problem: How Many Cycles?

Differential Equation Models ◽

10.1007/978-1-4612-5427-0_19 ◽

1983 ◽

pp. 279-297 ◽

Author(s):

Courtney S. Coleman

Keyword(s):

Hilbert’S 16Th Problem ◽

Hilbert's 16Th Problem

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Application (I)—Hilbert’s 16th Problem

Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles - Applied Mathematical Sciences ◽

10.1007/978-1-4471-2918-9_4 ◽

2012 ◽

pp. 81-212

Author(s):

Maoan Han ◽

Pei Yu

Keyword(s):

Hilbert’S 16Th Problem ◽

Hilbert's 16Th Problem

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Hilbert's 16th problem for classical Liénard equations of even degree

Journal of Differential Equations ◽

10.1016/j.jde.2007.11.011 ◽

2008 ◽

Vol 244 (6) ◽

pp. 1359-1394 ◽

Author(s):

M. Caubergh ◽

F. Dumortier

Keyword(s):

Liénard Equations ◽

Hilbert’S 16Th Problem ◽

Hilbert's 16Th Problem

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A Preparation Theorem for a Class of Non-differentiable Functions with an Application to Hilbert’s 16th Problem

Springer Proceedings in Mathematics & Statistics - Mathematical Sciences with Multidisciplinary Applications ◽

10.1007/978-3-319-31323-8_8 ◽

2016 ◽

pp. 133-177

Author(s):

Mohamed El Morsalani ◽

Abderaouf Mourtada

Keyword(s):

Hilbert’S 16Th Problem ◽

Differentiable Functions ◽

Preparation Theorem ◽

Hilbert's 16Th Problem

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Computation of limit cycles–The second part of Hilbert’s 16th problem

Bifurcation Theory and Spatio-Temporal Pattern Formation ◽

10.1090/fic/049/07 ◽

2006 ◽

pp. 151-177 ◽

Author(s):

Pei Yu

Keyword(s):

Limit Cycles ◽

Hilbert’S 16Th Problem ◽

Hilbert's 16Th Problem

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Nine Papers on Hilbert’s 16th Problem

10.1090/trans2/112 ◽

1978 ◽

Author(s):

D. Gudkov ◽

G. Utkin

Keyword(s):

Hilbert’S 16Th Problem ◽

Hilbert's 16Th Problem

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A Restricted Version of Hilbert's 16th Problem for Quadratic Vector Fields

Moscow Mathematical Journal ◽

10.17323/1609-4514-2010-10-2-317-335 ◽

2010 ◽

Vol 10 (2) ◽

pp. 317-335 ◽

Author(s):

Yu. Ilyashenko ◽

J. Llibre

Keyword(s):

Vector Fields ◽

Restricted Version ◽

Quadratic Vector Fields ◽

Hilbert’S 16Th Problem ◽

Hilbert's 16Th Problem

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On some open problems in planar differential systems and Hilbert’s 16th problem

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2005.10.057 ◽

2007 ◽

Vol 31 (5) ◽

pp. 1118-1134 ◽

Author(s):

Jaume Giné

Keyword(s):

Open Problems ◽

Differential Systems ◽

Hilbert’S 16Th Problem ◽

Hilbert's 16Th Problem

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On the second part of Hilbert's 16th problem

Nonlinear Analysis ◽

10.1016/j.na.2004.02.001 ◽

2004 ◽

Vol 57 (1) ◽

pp. 1

Author(s):

E. Oxenhielm

Keyword(s):

Hilbert’S 16Th Problem ◽

Hilbert's 16Th Problem

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HILBERT'S 16TH PROBLEM FOR QUADRATIC SYSTEMS: NEW METHODS BASED ON A TRANSFORMATION TO THE LIENARD EQUATION

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127408020732 ◽

2008 ◽

Vol 18 (03) ◽

pp. 877-884 ◽

Author(s):

G. LEONOV

Keyword(s):

Quadratic System ◽

Liénard Equation ◽

Two Dimensional ◽

Quadratic Systems ◽

Hilbert’S 16Th Problem ◽

New Methods ◽

Lienard Equation ◽

Hilbert's 16Th Problem ◽

Existence Criteria

Fractionally-quadratic transformations which reduce any two-dimensional quadratic system to the special Lienard equation are introduced. Existence criteria of cycles are obtained.

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Subanaliticity and the second part of Hilbert's 16th problem

Lecture Notes in Mathematics - Real Algebraic Geometry ◽

10.1007/bfb0084622 ◽

2006 ◽

pp. 221-234

Author(s):

Zofia Denkowska

Keyword(s):

Hilbert’S 16Th Problem ◽

Hilbert's 16Th Problem

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