Douglas S. Shafer

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All published works

Action	Title	Year	Authors
+ PDF Chat	Center cyclicity of Lorenz, Chen and Lü systems	2019	Isaac A. García Susanna Maza Douglas S. Shafer
+ PDF Chat	Centers and limit cycles in polynomial systems of ordinary differential equations	2019	Valery G. Romanovski Douglas S. Shafer
+	Cyclicity of polynomial nondegenerate centers on center manifolds	2018	Isaac A. García Susanna Maza Douglas S. Shafer
+	Asymptotics and stability of the delayed Duffing equation	2018	David Hill Douglas S. Shafer
+	SEPARATRIX AND LIMIT CYCLES OF	2016	Quadratic Systems Sieve Theorem Carmen Chicone Douglas S. Shafer
+	Symbolic Iterative Solution of Volterra Integral Equations	2016	Hamid Semiyari Douglas S. Shafer
+ PDF Chat	Cyclicity of a class of polynomial nilpotent center singularities	2015	Isaac A. García Douglas S. Shafer
+	Complete integrability and time-reversibility of some 3-dim systems	2015	Valery G. Romanovski Douglas S. Shafer
+	Bifurcation of critical periods of polynomial systems	2015	Brigita Ferčec Viktor Levandovskyy Valery G. Romanovski Douglas S. Shafer
+	Computation of focus quantities of three-dimensional polynomial systems	2014	Valery G. Romanovski Douglas S. Shafer
+	Properties of Monodromic Points on Center Manifolds in $${\mathbb {R}}^3$$ R 3 via Lie Symmetries	2013	Isaac A. García Susanna Maza Douglas S. Shafer
+	Introductory Statistics: Saylor	2013	Douglas S. Shafer Zhiyi Zhang
+ PDF Chat	Stability and periodic oscillations in the Moon–Rand systems	2012	Adam Mahdi Valery G. Romanovski Douglas S. Shafer
+	The 1: −q resonant center problem for certain cubic Lotka–Volterra systems	2012	Xingwu Chen Jaume Giné Valery G. Romanovski Douglas S. Shafer
+	Symbolic computation and the cyclicity problem for singularities	2011	Douglas S. Shafer
+	The center problem on a center manifold in	2011	V. F. Edneral Adam Mahdi Valery G. Romanovski Douglas S. Shafer
+	Leonid Antonovich Cherkas	2011	В. В. Амелькин A. F. Andreev И. В. Гайшун V. I. Gromak В. А. Ильин N. A. Izobov И. Т. Кигурадзе Jaume Llibre V. I. Mironenko В. А. Плисс
+ PDF Chat	Centers on center manifolds in the Lü system	2011	Adam Mahdi Claudio Pessoa Douglas S. Shafer
+	The Center and Cyclicity Problems: A Computational Algebra Approach	2009	Valery G. Romanovski Douglas S. Shafer
+	The Isochronicity and Linearizability Problems	2009	Valery G. Romanovski Douglas S. Shafer
+	Bifurcations of Limit Cycles and Critical Periods	2009	Valery G. Romanovski Douglas S. Shafer
+	The Center and Cyclicity Problems	2009	Douglas S. Shafer Valery G. Romanovski
+	Stability and Normal Forms	2009	Valery G. Romanovski Douglas S. Shafer
+	Polynomial Ideals and Their Varieties	2009	Valery G. Romanovski Douglas S. Shafer
+	The Center Problem	2009	Valery G. Romanovski Douglas S. Shafer
+	On the Center Problem for $p:-q$ Resonant Polynomial Vector Fields	2008	Valery G. Romanovski Douglas S. Shafer
+	The cyclicity of a cubic system with nonradical Bautin ideal	2008	Viktor Levandovskyy Valery G. Romanovski Douglas S. Shafer
+	<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mo>−</mml:mo><mml:mn>3</mml:mn></mml:math> resonant centers on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">C</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> with homogeneous cubic nonlinearities	2008	Zhaoping Hu Valery G. Romanovski Douglas S. Shafer
+	Structurally Stable Quadratic Foliations	2008	Xavier Jarque Jaume Llibre Douglas S. Shafer
+	Time-Reversibility in Two-Dimensional Polynomial Systems	2006	Valery G. Romanovski Douglas S. Shafer
+	Time-Reversibility i nT wo-D imensional Polynomial Systems	2006	Valery G. Romanovski Douglas S. Shafer
+	Integral invariants and limit sets of planar vector fields	2005	Isaac A. García Douglas S. Shafer
+	Structural Stability of Planar Polynomial Foliations	2005	Xavier Jarque Jaume Llibre Douglas S. Shafer
+	LIMIT SETS OF PLANAR VECTOR FIELDS AND THE VANISHING SET OF INVERSE INTEGRATING FACTORS	2005	Isaac A. García Douglas S. Shafer
+	Weak Singularities of Planar Vector Fields Under Weak Perturbation	2004	Douglas S. Shafer
+	Vertices of planar curves under the action of linear transformations	2002	Douglas S. Shafer Andr x E Zegeling
+	Geometry of cycles in quadratic systems	2002	Douglas S. Shafer André Zegeling
+	Any two quadratic cycles can be connected with a smooth arc	2000	Douglas S. Shafer André Zegeling
+	A Numerical Approach to Bifurcations from Quadratic Centers	1996	Douglas S. Shafer Xiaonan Wu André Zegeling
+	Bifurcation of Limit Cycles from Quadratic Centers	1995	Douglas S. Shafer André Zegeling
+	Finiteness Theorems for Limit Cycles	1993	Douglas S. Shafer
+	Multiple bifurcation in a predator–prey system with nonmonotonic predator response	1992	Franz Rothe Douglas S. Shafer
+	Restrictions on the Equivalence Homeomorphism in Stability of Polynomial Vector Fields	1990	Freddy Dumortier Douglas S. Shafer
+	Structure and Stability of Gradient Polynomial Vector Fields	1990	Douglas S. Shafer
+	Bifurcation in a quartic polynomial system arising in biology	1990	Franz Rothe Douglas S. Shafer
+ PDF Chat	Structural Stability and Generic Properties of Planar Polynomial Vector Fields	1987	Douglas S. Shafer
+	Topological hyperbolicity and the Coleman Conjecture for diffeomorphisms	1987	Douglas S. Shafer R. C. Swanson Russell B. Walker
+	Topological conjugacy of singularities of vector fields	1986	Douglas S. Shafer R. C. Swanson Russell B. Walker
+	Separatrix and Limit Cycles of Quadratic Systems and Dulac's Theorem	1983	Carmen Chicone Douglas S. Shafer
+	Singularities of gradient vectorfields in R3	1983	Douglas S. Shafer
+ PDF Chat	Separatrix and limit cycles of quadratic systems and Dulac’s theorem	1983	Carmen Chicone Douglas S. Shafer
+ PDF Chat	Quadratic Morse-Smale Vector Fields which are not Structurally Stable	1982	Carmen Chicone Douglas S. Shafer
+ PDF Chat	Quadratic Morse-Smale vector fields which are not structurally stable	1982	Carmen Chicone Douglas S. Shafer
+ PDF Chat	Topological Equivalence of Gradient Vectorfields	1980	Douglas S. Shafer
+ PDF Chat	Topological equivalence of gradient vectorfields	1980	Douglas S. Shafer
+	Gradient vectorfields near degenerate singularities	1980	Douglas S. Shafer

Common Coauthors

Coauthor	Papers Together
Valery G. Romanovski	19
Isaac A. García	6
André Zegeling	5
Carmen Chicone	5
Susanna Maza	3
Adam Mahdi	3
Jaume Llibre	3
Xavier Jarque	2
Franz Rothe	2
Viktor Levandovskyy	2
R. C. Swanson	2
Russell B. Walker	2
Hamid Semiyari	1
David Hill	1
В. В. Амелькин	1
Henryk Żołądek	1
Jaume Giné	1
V. I. Mironenko	1
Freddy Dumortier	1
И. В. Гайшун	1
V. F. Edneral	1
И. Н. Сергеев	1
Claudio Pessoa	1
Sieve Theorem	1
Quadratic Systems	1
Brigita Ferčec	1
W. Zhang	1
Zhiyi Zhang	1
Andr x E Zegeling	1
Xiaonan Wu	1
К. R. Schneider	1
Н. Х. Розов	1
В. А. Ильин	1
И. Т. Кигурадзе	1
Zhaoping Hu	1
А. П. Садовский	1
Nicolae Vulpe	1
A. F. Andreev	1
N. A. Izobov	1
Xingwu Chen	1
V. I. Gromak	1
T. K. Shemyakina	1
V. G. Romanovskii	1
В. А. Плисс	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	The Center and Cyclicity Problems: A Computational Algebra Approach	2009	Valery G. Romanovski Douglas S. Shafer	9
+ PDF Chat	Local Theory of Nonlinear Analytic Ordinary Differential Equations	1979	Yuri N. Bibikov	9
+ PDF Chat	Partial Differential Equations	1988	Shiing-Shen Chern	7
+	Singularities of vector fields on the plane	1977	Freddy Dumortier	7
+ PDF Chat	Ordinary Differential Equations with Applications	1999	Carmen Chicone	7
+ PDF Chat	Singularities of vector fields	1974	Floris Takens	7
+	Ordinary Differential Equations	2002	Philip Hartman	6
+	Differential Topology	1976	Morris W. Hirsch	5
+	A classical approach to the analyticity problem of center manifolds	1985	Bernd Aulbach	5
+	THEORY OF VALUES OF SINGULAR POINT IN COMPLEX AUTONOMOUS DIFFERENTIAL SYSTEMS	1990	Liu Yi-Reng LI Ji-Ban	5
+ PDF Chat	Properties of center manifolds	1985	Jan Sijbrand	5
+	The centre and isochronicity problems for some cubic systems	2001	Valery G. Romanovski Marko Robnik	5
+	Existence of inverse Jacobi multipliers around Hopf points in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math>: Emphasis on the center problem	2012	Adriana Buică Isaac A. García Susanna Maza	4
+ PDF Chat	Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem	1998	Robert Roussarie	4
+	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	4
+	The Cyclicity of a Cubic System	2009	Viktor Levandovskyy Alessandro Logar Valery G. Romanovski	4
+	Ordinary Differential Equations	2017	John M. Stewart	4
+ PDF Chat	Generic properties of polynomial vector fields at infinity	1969	Enrique A. González Velasco	4
+	Introduction to the Algebraic Theory of Invariants of Differential Equations	1989	Konstantin Sergeevich Sibirskiĭ	4
+	The center problem on a center manifold in	2011	V. F. Edneral Adam Mahdi Valery G. Romanovski Douglas S. Shafer	4
+	Generic Properties of Polynomial Vector Fields at Infinity	1969	Enrique A. Gonzalez Velasco	4
+ PDF Chat	Structural Stability and Generic Properties of Planar Polynomial Vector Fields	1987	Douglas S. Shafer	4
+	Smooth conjugacy of centre manifolds	1992	Almut Burchard Bo Deng Kening Lu	4
+	A survey of quadratic systems	1966	W. A. Coppel	4
+	A Singular Introduction to Commutative Algebra	2007	Gert–Martin Greuel Gerhard Pfister	3
+	Classification of generic quadratic vector fields with no limit cycles	1977	Geovan Tavares dos Santos	3
+	Theory of Limit Cycles	1986	Yan-Qian Ye Chi Lo	3
+	Qualitative theory of differential equations	1961		3
+	Ideals, Varieties, and Algorithms	1992	David Cox John B. Little Donal O’Shea	3
+	FORMULAS OF VALUES OF SINGULAR POINT AND THE INTEGRABILITY CONDITIONS FOR A CLASS OF CUBIC SYSTEM, M(3)≥7	1990	Liu Y	3
+ PDF Chat	Chordal quadratic systems	1986	Armengol Gasull Sheng Li-ren Jaume Llibre	3
+	Bifurcation of critical periods of polynomial systems	2015	Brigita Ferčec Viktor Levandovskyy Valery G. Romanovski Douglas S. Shafer	3
+ PDF Chat	Classification of continuous flows on 2-manifolds	1975	Dean A. Neumann	3
+ PDF Chat	Topological equivalence of gradient vectorfields	1980	Douglas S. Shafer	3
+ PDF Chat	Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in $\mathbb{C}^2$	2001	Colin Christopher Christiane Rousseau	3
+	Time-Reversibility in 2-Dimensional Systems	2008	Valery G. Romanovski	3
+ PDF Chat	Lectures on Analytic Differential Equations	2007	Yu. Ilyashenko Sergeî Yakovenko	3
+	Topological conjugacy of singularities of vector fields	1986	Douglas S. Shafer R. C. Swanson Russell B. Walker	3
+	The problem of center for resonant singular points of polynomial vector fields	1997	Henryk Żołądek	3
+	Qualitative Theory of Differential Equations	1961	Viktor Vladimirovich Nemytskii	2
+	Structural Stability of Planar Polynomial Foliations	2005	Xavier Jarque Jaume Llibre Douglas S. Shafer	2
+ PDF Chat	Global structure of ordinary differential equations in the plane	1954	Lawrence Markus	2
+	None	2003	Colin Christopher Pavao Mardešić Christiane Rousseau	2
+	The Sibirsky component of the center variety of polynomial differential systems	2003	Abdul Salam Jarrah Reinhard Laubenbacher Valery G. Romanovski	2
+	Bifurcations and trajectories joining critical points	1975	Nancy Kopell L. N. Howard	2
+	Analytic normalization of analytic integrable systems and the embedding flows	2008	Xiang Zhang	2
+	Polynomial Systems from Certain Differential Equations	1999	Dongming Wang	2
+	The cyclicity of a cubic system with nonradical Bautin ideal	2008	Viktor Levandovskyy Valery G. Romanovski Douglas S. Shafer	2
+	Cubic Vector Fields Symmetrical with Respect to a Center	1995	Christiane Rousseau Dana Schlomiuk	2
+ PDF Chat	Stability and periodic oscillations in the Moon–Rand systems	2012	Adam Mahdi Valery G. Romanovski Douglas S. Shafer	2