A Simple Proof for the Unicity of the Limit Cycle in the Bogdanov-Takens System

Li, Chengzhi ; Rousseau, Christiane ; Wang, Xian

Canadian mathematical bulletin, Tome 33 (1990) no. 1, pp. 84-92

Résumé

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.

Détail

DOI : 10.4153/CMB-1990-015-3

Mots-clés : 34C05, 34C35, 39

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