Abelian integrals for cubic vector fields
Copyright policy )Abelian integrals for cubic vector fields
The authors prove that the lowest upper bound of the number of the isolated zeros to the Abelian integral \[ I(h)= \oint_{\Gamma_h}(\alpha+ \beta x+\gamma x^2)y dx \] is two for \(h\in (-1/12,0)\), where \(\Gamma_h\) is the compact component of \(H(x, y)= (1/2)y^2+ (1/3) x^3+ (1/4)x^4= h,\alpha, \beta,\gamma\) are arbitrary constants.
- Peking University China (People's Republic of)
- Peking University China (People's Republic of)
Bifurcation theory for ordinary differential equations, Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.), perturbed system, bifurcation, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Homoclinic and heteroclinic solutions to ordinary differential equations, number of limit cycles
Bifurcation theory for ordinary differential equations, Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.), perturbed system, bifurcation, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Homoclinic and heteroclinic solutions to ordinary differential equations, number of limit cycles
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