Geodesic
A Simple Proof for the Unicity of the Limit Cycle in the Bogdanov-Takens System
Canadian mathematical bulletin, Tome 33 (1990) no. 1, pp. 84-92

Voir la notice de l'article provenant de la source Cambridge

DOI

We show that the Bogdanov-Takens system has at most one limit cycle. Similarly we show that the maximum number of limit cycles in the universal unfolding of the symmetric cusp of order 2 (resp. 3) is one (resp. 2). The proof uses the elementary technique of Liénard's equation, yielding a global result for all values of the parameters.
DOI : 10.4153/CMB-1990-015-3
Mots-clés : 34C05, 34C35, 39 
Li, Chengzhi; Rousseau, Christiane; Wang, Xian. A Simple Proof for the Unicity of the Limit Cycle in the Bogdanov-Takens System. Canadian mathematical bulletin, Tome 33 (1990) no. 1, pp. 84-92. doi: 10.4153/CMB-1990-015-3
@article{10_4153_CMB_1990_015_3,
     author = {Li, Chengzhi and Rousseau, Christiane and Wang, Xian},
     title = {A {Simple} {Proof} for the {Unicity} of the {Limit} {Cycle} in the {Bogdanov-Takens} {System}},
     journal = {Canadian mathematical bulletin},
     pages = {84--92},
     year = {1990},
     volume = {33},
     number = {1},
     doi = {10.4153/CMB-1990-015-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-015-3/}
}
TY  - JOUR
AU  - Li, Chengzhi
AU  - Rousseau, Christiane
AU  - Wang, Xian
TI  - A Simple Proof for the Unicity of the Limit Cycle in the Bogdanov-Takens System
JO  - Canadian mathematical bulletin
PY  - 1990
SP  - 84
EP  - 92
VL  - 33
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-015-3/
DO  - 10.4153/CMB-1990-015-3
ID  - 10_4153_CMB_1990_015_3
ER  - 
%0 Journal Article
%A Li, Chengzhi
%A Rousseau, Christiane
%A Wang, Xian
%T A Simple Proof for the Unicity of the Limit Cycle in the Bogdanov-Takens System
%J Canadian mathematical bulletin
%D 1990
%P 84-92
%V 33
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-015-3/
%R 10.4153/CMB-1990-015-3
%F 10_4153_CMB_1990_015_3

Cité par Sources :