Perturbation from an elliptic Hamiltonian of degree four—III global centre
By Freddy Dumortier, Chengzhi Li. 2003
75 citations recorded by the source corpus.
Abstract The paper deals with Lienard equations of the form x =y , y =P(x)+yQ(x) with P and Q polynomials of degree, respectively, 3 and 2. Attention goes to perturbations of the Hamiltonian vector fields with an elliptic Hamiltonian of degree four, exhibiting a global centre. It is proven that the least upper bound of the number of zeros of the related elliptic integral is four, and this is a sharp one. This result permits to prove the existence of Lienard equations of type (3,2) with a quadruple limit cycle, with both a triple and a simple limit cycle, with two semistable limit cycles, with one semistable and two simple limit cycles or with four simple limit cycles.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/8277475ea62850328fc15652ca5de4fa8f8bb5d2
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In Geometry and Topology
- Chengzhi Li
- Jaume Llibre
- Fengde Chen
- Zenghua Zhang
- Xiang Zhang
- Maite Grau
- Douglas Duarte Novaes
- Maoan Han
Citations in the corpus
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