Keyword

planar vector fields

Description: Vector fields defined on a two-dimensional plane, used to describe continuous dynamical systems and analyze their equilibria, cycles, and bifurcations.

Primary topic: Advanced Differential Equations and Dynamical Systems (82%)

OpenAlex ID: keywords/planar-vector-fields

Normal Forms and Bifurcation of Planar Vector Fields

1994 · Shui-Nee Chow, Chengzhi Li, et al. · Cambridge University Press eBooks · 728

Relaxation Oscillation and Canard Explosion

2001 · M. Krupa, P. Szmolyan · Journal of Differential Equations · 516

Bifurcation Sets of Continuous Piecewise Linear Systems with Two Zones

1998 · Emilio Freire, Enrique Ponce, et al. · International Journal of Bifurcation and Chaos · 282

Singularities of vector fields on the plane

1977 · Freddy Dumortier · Journal of Differential Equations · 253

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On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields

1986 · R. Roussarie · Bulletin of the Brazilian Mathematical Society New Series · 244

Versal deformations of a singular point of a vector field on the plane in the case of zero eigenvalues

1975 · R. I. Bogdanov · Functional Analysis and Its Applications · 240

A survey of isochronous centers

1999 · Javier Chavarriga, Marco Sabatini · Qualitative Theory of Dynamical Systems · 225

Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem

1998 · Robert Roussarie · Modern Birkhäuser classics · 210

Bifurcation of Planar Vector Fields and Hilbert's Sixteenth Problem

1998 · Roussarie, Robert · Birkhäuser Basel eBooks · 184

Bounded Polynomial Vector Fields

1990 · Anna Cima, Jaume Llibre · Transactions of the American Mathematical Society · 181

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On a Poincaré-birkhoff Problem

1967 · L P Šil'nikov · Mathematics of the USSR-Sbornik · 175

Normal forms for certain singularities of vectorfields

1973 · Floris Takens · Annales de l’institut Fourier · 170

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On the nonexistence, existence and uniqueness of limit cycles

1996 · H Giacomini, J Llibre, et al. · Nonlinearity · 162

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Successive derivatives of a first return map, application to the study of quadratic vector fields

1996 · J. P. Francoise · Ergodic Theory and Dynamical Systems · 160

Direct Discretization of Planar Div-Curl Problems

1992 · R. A. Nicolaides · SIAM Journal on Numerical Analysis · 159

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Bifurcations of Planar Vector Fields

1991 · Freddy Dumortier, Robert Roussarie, et al. · Lecture notes in mathematics · 150

Finitely-smooth normal forms of local families of diffeomorphisms and vector fields

1991 · Yu S Il'yashenko, S Yu Yakovenko · Russian Mathematical Surveys · 139

Nonlinear Dynamics and Evolution Equations

2006 · Brunner, Hermann, Zhao, Xiao-Qiang, et al. · American Mathematical Society eBooks · 136

Symétrie et forme normale des centres et foyers dégénérés

1982 · Robert Moussu · Ergodic Theory and Dynamical Systems · 126

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A Survey on the Blow up Technique

2011 · MARÍA JESÚS ÁLVAREZ, ANTONI FERRAGUT, et al. · International Journal of Bifurcation and Chaos · 125

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Equivalence and Decomposition of Vector Fields About an Elementary Critical Point

1963 · Kuo-Tsai Chen · American Journal of Mathematics · 120

The Analytic and Formal Normal Form for the Nilpotent Singularity

2002 · Ewa Stróżyna, Henryk Żołądek · Journal of Differential Equations · 118

More limit cycles than expected in Liénard equations

2007 · Freddy Dumortier, Daniel Panazzolo, et al. · Proceedings of the American Mathematical Society · 102

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The Saddle-Node Separatrix-Loop Bifurcation

1987 · Stephen Schecter · SIAM Journal on Mathematical Analysis · 95

Continuous topology simplification of planar vector fields

2001 · Xavier Tricoche, Gerik Scheuermann, et al. · IEEE Visualization · 93

Works count: 1,281

Citation count: 12,850