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Linear type centers of polynomial Hamiltonian systems with nonlinearities of degree 4 symmetric with respect to the \(\mathrm{y}\)-axis. (English) Zbl 1440.34031

Summary: We provide the phase portraits in the Poincaré disk for all the linear type centers of polynomial Hamiltonian systems with nonlinearities of degree 4 symmetric with respect to the \(y\)-axis given by the Hamiltonian function \(H(x,y)=1/2(x^2+y^2)+ax^4y+bx^2y^3+cy^5\) in function of its parameters.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
37J51 Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods
34C25 Periodic solutions to ordinary differential equations
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