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Author ID: shafer.douglas-s Recent zbMATH articles by "Shafer, Douglas S."
Published as: Shafer, Douglas S.; Shafer, D. S.; Shafer, Douglas
Documents Indexed: 42 Publications since 1980, including 1 Book and 1 Additional arXiv Preprint
Reviewing Activity: 149 Reviews
Co-Authors: 22 Co-Authors with 34 Joint Publications
703 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

34 Publications have been cited 493 times in 343 Documents Cited by Year
The center and cyclicity problems. A computational algebra approach. Zbl 1192.34003
Romanovski, Valery G.; Shafer, Douglas S.
209
2009
The center problem on a center manifold in \(\mathbb{R}^{3}\). Zbl 1259.34021
Edneral, Victor F.; Mahdi, Adam; Romanovski, Valery G.; Shafer, Douglas S.
37
2012
The \({1:-q}\) resonant center problem for certain cubic Lotka-Volterra systems. Zbl 1365.34006
Chen, Xingwu; Giné, Jaume; Romanovski, Valery G.; Shafer, Douglas S.
19
2012
Separatrix and limit cycles of quadratic systems and Dulac’s theorem. Zbl 0522.58041
Chicone, Carmen; Shafer, Douglas S.
18
1983
Multiple bifurcation in a predator-prey system with non-monotonic predator response. Zbl 0763.92011
Rothe, Franz; Shafer, Douglas S.
16
1992
Integral invariants and limit sets of planar vector fields. Zbl 1092.34013
García, Isaac A.; Shafer, Douglas S.
16
2005
On the center problem for \(p:-q\) resonant polynomial vector fields. Zbl 1163.34020
Romanovski, Valery G.; Shafer, Douglas S.
15
2008
\(1: - 3\) resonant centers on \(\mathbb{C}^2\) with homogeneous cubic nonlinearities. Zbl 1165.34334
Hu, Zhaoping; Romanovski, Valery G.; Shafer, Douglas S.
15
2008
Bifurcation of limit cycles from quadratic centers. Zbl 0833.34029
Shafer, Douglas S.; Zegeling, André
14
1995
Bifurcation of critical periods of polynomial systems. Zbl 1337.34032
Ferčec, Brigita; Levandovskyy, Viktor; Romanovski, Valery G.; Shafer, Douglas S.
14
2015
Centers on center manifolds in the Lü system. Zbl 1252.70046
Mahdi, Adam; Pessoa, Claudio; Shafer, Douglas S.
14
2011
Stability and periodic oscillations in the Moon-Rand systems. Zbl 1264.34059
Mahdi, Adam; Romanovski, Valery G.; Shafer, Douglas S.
14
2013
Cyclicity of polynomial nondegenerate centers on center manifolds. Zbl 1434.37030
García, Isaac A.; Maza, Susanna; Shafer, Douglas S.
12
2018
Center cyclicity of Lorenz, Chen and Lü systems. Zbl 1428.37046
García, Isaac A.; Maza, Susanna; Shafer, Douglas S.
9
2019
Cyclicity of a class of polynomial nilpotent center singularities. Zbl 1336.37041
García, Isaac A.; Shafer, Douglas S.
7
2016
Centers and limit cycles in polynomial systems of ordinary differential equations. Zbl 1383.34053
Romanovski, Valery G.; Shafer, Douglas S.
7
2016
The cyclicity of a cubic system with nonradical Bautin ideal. Zbl 1163.34019
Levandovskyy, Viktor; Romanovski, Valery G.; Shafer, Douglas S.
6
2009
Singularities of gradient vector-fields in \(R^ 3\). Zbl 0468.58017
Shafer, Douglas S.
5
1983
Structural stability and generic properties of planar polynomial vector fields. Zbl 0677.58029
Shafer, Douglas S.
5
1987
Asymptotics and stability of the delayed Duffing equation. Zbl 1395.34079
Hill, David C.; Shafer, Douglas S.
5
2018
Properties of monodromic points on center manifolds in \(\mathbb R^3\) via Lie symmetries. Zbl 1311.37036
García, Isaac A.; Maza, Susanna; Shafer, Douglas S.
5
2013
Structure and stability of gradient polynomial vector fields. Zbl 0661.58016
Shafer, Douglas S.
4
1990
Structural stability of planar polynomial foliations. Zbl 1091.34031
Jarque, Xavier; Llibre, Jaume; Shafer, Douglas S.
4
2005
Symbolic computation and the cyclicity problem for singularities. Zbl 1259.34002
Shafer, Douglas S.
4
2012
Restrictions on the equivalence homeomorphism in stability of polynomial vector fields. Zbl 0664.58021
Dumortier, Freddy; Shafer, Douglas S.
3
1990
Topological conjugacy of singularities of vector fields. Zbl 0622.58036
Shafer, Douglas S.; Swanson, Richard C.; Walker, Russell B.
3
1986
Time-reversibility in two-dimensional polynomial systems. Zbl 1110.34026
Romanovski, Valery G.; Shafer, Douglas S.
3
2005
Any two quadratic cycles can be connected with a smooth arc. Zbl 0945.34019
Shafer, Douglas S.; Zegeling, André
2
2000
Vertices of planar curves under the action of linear transformations. Zbl 1011.53002
Shafer, Douglas S.; Zegeling, André
2
2002
Structurally stable quadratic foliations. Zbl 1170.34038
Jarque, Xavier; Llibre, Jaume; Shafer, Douglas S.
2
2008
Quadratic Morse-Smale vector fields which are not structurally stable. Zbl 0504.58026
Chicone, Carmen; Shafer, Douglas S.
1
1982
A numerical approach to bifurcations from quadratic centers. Zbl 0860.65061
Shafer, Douglas S.; Wu, Xiaonan; Zegeling, André
1
1996
Complete integrability and time-reversibility of some 3-dim systems. Zbl 1334.34007
Romanovski, Valery G.; Shafer, Douglas S.
1
2016
Topological equivalence of gradient vectorfields. Zbl 0426.58015
Shafer, Douglas S.
1
1980
Center cyclicity of Lorenz, Chen and Lü systems. Zbl 1428.37046
García, Isaac A.; Maza, Susanna; Shafer, Douglas S.
9
2019
Cyclicity of polynomial nondegenerate centers on center manifolds. Zbl 1434.37030
García, Isaac A.; Maza, Susanna; Shafer, Douglas S.
12
2018
Asymptotics and stability of the delayed Duffing equation. Zbl 1395.34079
Hill, David C.; Shafer, Douglas S.
5
2018
Cyclicity of a class of polynomial nilpotent center singularities. Zbl 1336.37041
García, Isaac A.; Shafer, Douglas S.
7
2016
Centers and limit cycles in polynomial systems of ordinary differential equations. Zbl 1383.34053
Romanovski, Valery G.; Shafer, Douglas S.
7
2016
Complete integrability and time-reversibility of some 3-dim systems. Zbl 1334.34007
Romanovski, Valery G.; Shafer, Douglas S.
1
2016
Bifurcation of critical periods of polynomial systems. Zbl 1337.34032
Ferčec, Brigita; Levandovskyy, Viktor; Romanovski, Valery G.; Shafer, Douglas S.
14
2015
Stability and periodic oscillations in the Moon-Rand systems. Zbl 1264.34059
Mahdi, Adam; Romanovski, Valery G.; Shafer, Douglas S.
14
2013
Properties of monodromic points on center manifolds in \(\mathbb R^3\) via Lie symmetries. Zbl 1311.37036
García, Isaac A.; Maza, Susanna; Shafer, Douglas S.
5
2013
The center problem on a center manifold in \(\mathbb{R}^{3}\). Zbl 1259.34021
Edneral, Victor F.; Mahdi, Adam; Romanovski, Valery G.; Shafer, Douglas S.
37
2012
The \({1:-q}\) resonant center problem for certain cubic Lotka-Volterra systems. Zbl 1365.34006
Chen, Xingwu; Giné, Jaume; Romanovski, Valery G.; Shafer, Douglas S.
19
2012
Symbolic computation and the cyclicity problem for singularities. Zbl 1259.34002
Shafer, Douglas S.
4
2012
Centers on center manifolds in the Lü system. Zbl 1252.70046
Mahdi, Adam; Pessoa, Claudio; Shafer, Douglas S.
14
2011
The center and cyclicity problems. A computational algebra approach. Zbl 1192.34003
Romanovski, Valery G.; Shafer, Douglas S.
209
2009
The cyclicity of a cubic system with nonradical Bautin ideal. Zbl 1163.34019
Levandovskyy, Viktor; Romanovski, Valery G.; Shafer, Douglas S.
6
2009
On the center problem for \(p:-q\) resonant polynomial vector fields. Zbl 1163.34020
Romanovski, Valery G.; Shafer, Douglas S.
15
2008
\(1: - 3\) resonant centers on \(\mathbb{C}^2\) with homogeneous cubic nonlinearities. Zbl 1165.34334
Hu, Zhaoping; Romanovski, Valery G.; Shafer, Douglas S.
15
2008
Structurally stable quadratic foliations. Zbl 1170.34038
Jarque, Xavier; Llibre, Jaume; Shafer, Douglas S.
2
2008
Integral invariants and limit sets of planar vector fields. Zbl 1092.34013
García, Isaac A.; Shafer, Douglas S.
16
2005
Structural stability of planar polynomial foliations. Zbl 1091.34031
Jarque, Xavier; Llibre, Jaume; Shafer, Douglas S.
4
2005
Time-reversibility in two-dimensional polynomial systems. Zbl 1110.34026
Romanovski, Valery G.; Shafer, Douglas S.
3
2005
Vertices of planar curves under the action of linear transformations. Zbl 1011.53002
Shafer, Douglas S.; Zegeling, André
2
2002
Any two quadratic cycles can be connected with a smooth arc. Zbl 0945.34019
Shafer, Douglas S.; Zegeling, André
2
2000
A numerical approach to bifurcations from quadratic centers. Zbl 0860.65061
Shafer, Douglas S.; Wu, Xiaonan; Zegeling, André
1
1996
Bifurcation of limit cycles from quadratic centers. Zbl 0833.34029
Shafer, Douglas S.; Zegeling, André
14
1995
Multiple bifurcation in a predator-prey system with non-monotonic predator response. Zbl 0763.92011
Rothe, Franz; Shafer, Douglas S.
16
1992
Structure and stability of gradient polynomial vector fields. Zbl 0661.58016
Shafer, Douglas S.
4
1990
Restrictions on the equivalence homeomorphism in stability of polynomial vector fields. Zbl 0664.58021
Dumortier, Freddy; Shafer, Douglas S.
3
1990
Structural stability and generic properties of planar polynomial vector fields. Zbl 0677.58029
Shafer, Douglas S.
5
1987
Topological conjugacy of singularities of vector fields. Zbl 0622.58036
Shafer, Douglas S.; Swanson, Richard C.; Walker, Russell B.
3
1986
Separatrix and limit cycles of quadratic systems and Dulac’s theorem. Zbl 0522.58041
Chicone, Carmen; Shafer, Douglas S.
18
1983
Singularities of gradient vector-fields in \(R^ 3\). Zbl 0468.58017
Shafer, Douglas S.
5
1983
Quadratic Morse-Smale vector fields which are not structurally stable. Zbl 0504.58026
Chicone, Carmen; Shafer, Douglas S.
1
1982
Topological equivalence of gradient vectorfields. Zbl 0426.58015
Shafer, Douglas S.
1
1980
all top 5

Cited by 307 Authors

50 Giné, Jaume
50 Romanovskiĭ, Valeriĭ Georgievich
31 García, Isaac A.
19 Algaba, Antonio
19 Ferčec, Brigita
17 Llibre, Jaume
16 García, Cristóbal
15 Huang, Wentao
15 Shafer, Douglas S.
15 Valls Anglés, Cláudia
15 Zhang, Weinian
13 Han, Maoan
12 Maza, Susanna
12 Torregrosa, Joan
12 Zhang, Xiang
11 Chen, Xingwu
9 Oliveira, Regilene D. S.
8 Reyes, Manuel
8 Wang, Qinlong
8 Yu, Zhiheng
7 Li, Feng
7 Liu, Yirong
7 Mencinger, Matej
6 Fernandes, Wilker
6 Huang, Bo
6 Pessoa, Claudio
6 Tang, Yilei
6 Zegeling, André
5 Dukarić, Maša
5 Li, Chengzhi
5 Mahdi, Adam
5 Sánchez-Sánchez, Iván
5 Wu, Yusen
4 Aybar, Orhan Ozgur
4 Buică, Adriana
4 Buzzi, Claudio Aguinaldo
4 Du, Chaoxiong
4 Dumortier, Freddy
4 Edneral, Victor F.
4 Fuentes, Natalia
4 Grau, Maite
4 Liu, Lingling
4 Queiroz, Lucas
4 Sang, Bo
4 Zhao, Yulin
3 Boros, Balázs
3 Boussaada, Islam
3 Bravo, José Luis
3 Chen, Yufu
3 Dong, Guangfeng
3 Fernandez García-Hierro, Manuel
3 Fernández-Sánchez, Fernando
3 Giacomini, Hector J.
3 Gouveia, Luiz F. S.
3 Guo, Laigang
3 Hofbauer, Josef
3 Hu, Zhaoping
3 Kooij, Robert E.
3 Li, Weigu
3 Liu, Changjian
3 Liu, Yuanyuan
3 Merino, Manuel
3 Novaes, Douglas Duarte
3 Perko, Lawrence M.
3 Petek, Tatjana
3 Rodríguez-Luis, Alejandro J.
3 Xia, Yonghui
3 Yu, Pei
3 Zhang, Zhifen
3 Zhou, Zhengxin
2 Arcet, Barbara
2 Aybar, Ilknur Kusbeyzi
2 Aziz, Waleed
2 Bardet, Magali
2 Bastos, Jéfferson L. R.
2 Bonckaert, Patrick
2 Čanić, Sunčica
2 Chicone, Carmen C.
2 Chouikha, Abd Raouf
2 Christopher, Colin J.
2 Feng, Jingjing
2 Ferragut, Antoni
2 Gamero, Estanislao
2 Gasull, Armengol
2 Gu, Jieping
2 Huang, Kaiyin
2 Iliev, Iliya Dimov
2 Jarque, Xavier
2 Levandovskyy, Viktor
2 Li, Lin
2 Li, Na
2 Li, Tao
2 Müller, Stefan
2 Ojeda Martínez de Castilla, Ignacio
2 Rabanal, Roland
2 Regensburger, Georg
2 Ribeiro, Jarne D.
2 Sadovskiĭ, Anton Pavlovich
2 Shcheglova, Tatsiana V.
2 Shi, Shaoyun
...and 207 more Authors
all top 5

Cited in 85 Serials

48 Journal of Differential Equations
25 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
23 Journal of Mathematical Analysis and Applications
19 Qualitative Theory of Dynamical Systems
18 Applied Mathematics and Computation
12 Nonlinear Analysis. Real World Applications
10 Chaos, Solitons and Fractals
9 Journal of Dynamics and Differential Equations
8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
8 Nonlinear Dynamics
7 Journal of Symbolic Computation
7 Applied Mathematics Letters
7 Discrete and Continuous Dynamical Systems
6 Mathematical Methods in the Applied Sciences
6 Communications in Nonlinear Science and Numerical Simulation
5 Journal of Computational and Applied Mathematics
5 Proceedings of the American Mathematical Society
5 Bulletin des Sciences Mathématiques
5 Discrete and Continuous Dynamical Systems. Series B
5 Communications on Pure and Applied Analysis
4 Buletinul Academiei de Științe a Republicii Moldova. Matematica
4 Differential Equations
4 Journal of Applied Analysis and Computation
3 Mathematics and Computers in Simulation
3 Programming and Computer Software
3 Acta Applicandae Mathematicae
3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
3 Journal of Nonlinear Science
3 Abstract and Applied Analysis
2 Computers & Mathematics with Applications
2 Physics Letters. A
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Proceedings of the Edinburgh Mathematical Society. Series II
2 Science in China. Series A
2 Chaos
2 Journal of Dynamical and Control Systems
2 Journal of Nonlinear Mathematical Physics
2 Dynamical Systems
2 Mediterranean Journal of Mathematics
2 Science China. Mathematics
1 Journal of Mathematical Biology
1 Mathematical Biosciences
1 Nonlinearity
1 Rocky Mountain Journal of Mathematics
1 Bulletin of Mathematical Biology
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 Publications Mathématiques
1 Metroeconomica
1 Results in Mathematics
1 Studies in Applied Mathematics
1 Transactions of the American Mathematical Society
1 Ergodic Theory and Dynamical Systems
1 Chinese Annals of Mathematics. Series B
1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
1 Physica D
1 Acta Mathematicae Applicatae Sinica. English Series
1 Glasnik Matematički. Serija III
1 SIAM Journal on Applied Mathematics
1 Bulletin of the American Mathematical Society. New Series
1 Expositiones Mathematicae
1 Experimental Mathematics
1 Topological Methods in Nonlinear Analysis
1 Journal of Mathematical Sciences (New York)
1 Electronic Journal of Differential Equations (EJDE)
1 Turkish Journal of Mathematics
1 NoDEA. Nonlinear Differential Equations and Applications
1 Journal of Lie Theory
1 Journal of Mathematical Chemistry
1 Open Systems & Information Dynamics
1 Acta Mathematica Sinica. English Series
1 Communications in Contemporary Mathematics
1 Differentsial’nye Uravneniya i Protsessy Upravleniya
1 Journal of Systems Science and Complexity
1 Journal of Applied Mathematics
1 Acta Mathematica Scientia. Series B. (English Edition)
1 Vestsi Natsyyanal’naĭ Akadèmii Navuk Belarusi. Seryya Fizika-Matèmatychnykh Navuk
1 MATCH - Communications in Mathematical and in Computer Chemistry
1 Advances in Difference Equations
1 Boundary Value Problems
1 Journal of Physics A: Mathematical and Theoretical
1 Discrete and Continuous Dynamical Systems. Series S
1 Advances in Nonlinear Analysis
1 Nonlinear Analysis. Theory, Methods & Applications
1 European Journal of Mathematics
1 AIMS Mathematics

Citations by Year