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Keyword

polynomial vector fields

Description: Vector fields whose component functions are polynomials, studied in dynamical systems, differential equations, and algebraic geometry.
OpenAlex ID: keywords/polynomial-vector-fields
Qualitative Theory of Planar Differential Systems
2006 · Dumortier, Freddy, Llibre, Jaume, et al. · Springer eBooks · 848
On the construction of Lyapunov functions using the sum of squares decomposition
2003 · A. Papachristodoulou, S. Prajna · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · 472
A survey of quadratic systems
1966 · W.A Coppel · Journal of Differential Equations · 272
Stability Region Analysis Using Polynomial and Composite Polynomial Lyapunov Functions and Sum-of-Squares Programming
2008 · Weehong Tan, Andrew Packard · IEEE Transactions on Automatic Control · 267
The Center and Cyclicity Problems: A Computational Algebra Approach
2009 · Valery G. Romanovski, Douglas S. Shafer · Medical Entomology and Zoology · 254
Local stability analysis using simulations and sum-of-squares programming
2008 · Ufuk Topcu, Andrew Packard, et al. · Automatica · 242
Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac
1992 · Jean Écalle · Hermann eBooks · 229
Multiplicity of invariant algebraic curves in polynomial vector fields
2007 · Colin Christopher, Jaume Llibre, et al. · Pacific Journal of Mathematics · 205
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Finiteness theorems for limit cycles
1990 · Yu S Il'yashenko · Russian Mathematical Surveys · 198
Some controls applications of sum of squares programming
2004 · Z. Jarvis-Wloszek, R. Feeley, et al. · 176
Generic Properties of Polynomial Vector Fields at Infinity
1969 · Enrique A. González Velasco · Transactions of the American Mathematical Society · 165
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Algorithmic Construction of Lyapunov Functions for Power System Stability Analysis
2013 · Marian Anghel, Federico Milano, et al. · IEEE Transactions on Circuits and Systems I Regular Papers · 160
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
On the number of solutions of the equation $$\frac{{dx}}{{dt}} = \sum\limits_{j = 0}^n {a_j (t) x^j ,0 \leqq t \leqq 1,} $$ for whichx(0)=x(1)
1980 · Alcides Lins Neto · Inventiones mathematicae · 148
A Concrete Example of the Existence of Four Limit Cycles for Plane Quadratic Systems
1980 · Shi Songling · Scientia Sinica · 147
Modeling and synchronizing chaotic systems from time-series data
1994 · Reggie Brown, Nikolai F. Rulkov, et al. · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 143
Linearization of Isochronous Centers
1995 · P. Mardesic, C. Rousseau, et al. · Journal of Differential Equations · 142
Control Applications of Sum of Squares Programming
2005 · Zachary Jarvis-Wloszek, Ryan Feeley, et al. · Lecture notes in control and information sciences · 133
A cubic system with thirteen limit cycles
2009 · Chengzhi Li, Changjian Liu, et al. · Journal of Differential Equations · 132
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Algebraic and Geometric Aspects of the Theory of Polynomial Vector Fields
1993 · Dana Schlomiuk · Springer eBooks · 127
The Poincare Problem in the Nondicritical Case
1994 · Manuel M. Carnicer · Annals of Mathematics · 123
Linear identification of nonlinear systems: A lifting technique based on the Koopman operator
2016 · Alexandre Mauroy, Jorge Goncalves · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · 118
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Darboux theory of integrability in Cn taking into account the multiplicity
2008 · Jaume Llibre, Xiang Zhang · Journal of Differential Equations · 118
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Perturbations from an Elliptic Hamiltonian of Degree Four
2001 · Freddy Dumortier, Chengzhi Li · Journal of Differential Equations · 118
Perturbations from an Elliptic Hamiltonian of Degree Four
2001 · Freddy Dumortier, Chengzhi Li · Journal of Differential Equations · 106
Works count: 1,926
Citation count: 17,340
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