Perturbation from an elliptic Hamiltonian of degree four—III global centre |
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Authors: | Freddy Dumortier Chengzhi Li |
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Institution: | a Limburgs Universitair Centrum, Universitaire Campus, B-3590 Diepenbeek, Belgium b Department of Mathematics, Peking University, Beijing 100871, China |
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Abstract: | The paper deals with Liénard equations of the form , 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 Liénard 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. |
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