On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems (Q651129)
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scientific article; zbMATH DE number 5987791
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems |
scientific article; zbMATH DE number 5987791 |
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On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems (English)
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8 December 2011
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The main task of the paper is to provide a complete investigation of the number and possible configurations of limit cycles for the following Liénard system \[ \dot{x} = y, \dot{y} = x(x-1)^3(x+1/2) + \varepsilon (a+bx+cx^3+x^4)y, \] where \(0<\varepsilon\ll 1\) and \(a, b,c\) are real parameters. The authors study the Hopf and Poincaré bifurcation of this system as well as the number of zeros of corresponding Abelian integrals for the center and for the heteroclinic loop.
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Liénard system
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16-th Hilbert's problem
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Abelian integral
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limit cycle
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