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Keyword

center-focus problem

Description: A problem in the qualitative theory of planar differential equations that determines whether a critical point is a center or a focus.
OpenAlex ID: keywords/center-focus-problem
Qualitative Theory of Planar Differential Systems
2006 · Dumortier, Freddy, Llibre, Jaume, et al. · Springer eBooks · 848
On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type
1954 · Nathalie Bautin · American Mathematical Society eBooks · 364
Integrability of Dynamical Systems: Algebra and Analysis
2017 · Xiang Zhang · Developments in mathematics · 107
The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
2006 · Hector Giacomini, Jaume Giné, et al. · Journal of Differential Equations · 99
Center-Focus Problem for Discontinuous Planar Differential Equations
2003 · Armengol Gasull, Joan Torregrosa · International Journal of Bifurcation and Chaos · 95
On the period function of x″+f(x)x′2+g(x)=0
2003 · M. Sabatini · Journal of Differential Equations · 77
Generating limit cycles from a nilpotent critical point via normal forms
2005 · M.J. Álvarez, A. Gasull · Journal of Mathematical Analysis and Applications · 76
Theory of center-focus for a class of higher-degree critical points and infinite points
2001 · Yirong Liu · Science in China Series A Mathematics · 75
Solution of the $1 : {−}2$ resonant center problem in the quadratic case
1998 · Alexandra Fronville, Anton P. Sadovski, et al. · Fundamenta Mathematicae · 73
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On a certain generalization of Bautin's theorem
1994 · H Zoladek · Nonlinearity · 63
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Classification and analysis of two-dimensional real homogeneous quadratic differential equation systems
1979 · Tsutomu Date · Journal of Differential Equations · 61
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Polynomial Liénard Equations near Infinity
1999 · Freddy Dumortier, Chris Herssens · Journal of Differential Equations · 55
On the structure of Poincaré-Lyapunov constants for the weak focus of polynomial vector fields
1984 · Shi Songling · Journal of Differential Equations · 52
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Integrability conditions for Lotka–Volterra planar complex quintic systems
2009 · Jaume Giné, Valery G. Romanovski · Nonlinear Analysis Real World Applications · 51
The Center-Focus Problem and Reversibility
2001 · Marco Antonio Teixeira, Jiazhong Yang · Journal of Differential Equations · 51
Remarks on "The classification of reversible cubic systems with center"
1996 · Henryk Żołądek · Topological Methods in Nonlinear Analysis · 48
A new algorithm for the computation of the Lyapunov constants for some degenerated critical points
2001 · Armengol Gasull, Joan Torregrosa · Nonlinear Analysis · 47
The Monotonicity of Period Function for Codimension Four Quadratic System Q4
2002 · Yulin Zhao · Journal of Differential Equations · 46
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The Center-Focus Problem for a System with Homogeneous Nonlinearities in the Case of Zero Eigenvalues of the Linear Part
2003 · A. F. Andreev, A. P. Sadovskii, et al. · Differential Equations · 44
Polynomial Hamiltonian systems with a nilpotent critical point
2009 · Maoan Han, Chenggang Shu, et al. · Advances in Space Research · 43
A Complete Classification on the Center-Focus Problem of a Generalized Cubic Kukles System with a Nilpotent Singular Point
2023 · Feng Li, Ting Chen, et al. · Qualitative Theory of Dynamical Systems · 36
Corrigendum to: “The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems” [J. Differential Equations 227 (2006) 406–426]
2006 · Hector Giacomini, Jaume Giné, et al. · Journal of Differential Equations · 36
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Conditions for a centre and the bifurcation of limit cycles in a class of cubic systems
1990 · NG Lloyd, JM Pearson · Lecture notes in mathematics · 36
Zum Zentrumproblem
1928 · Hubert Cremer · Mathematische Annalen · 36
Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields
2014 · Ilker E. Colak, Jaume Llibre, et al. · Journal of Differential Equations · 35
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Works count: 588
Citation count: 4,287
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