Cubic perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain (Q2335846)
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| English | Cubic perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain |
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Cubic perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain (English)
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15 November 2019
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In this paper, the authors consider arbitrary one-parameter cubic deformations of the Duffing oscillator \(x''=x-x^3\). Under the hypothesis that the first Melnikov function \(M_1\) is identically zero, they present an explicit formula for the second Melnikov function \(M_2\) and study its zeros in a suitable complex domain.
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limit cycles
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zeros of elliptic integrals
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Duffing oscillator
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