Polynomial Hamiltonian systems of degree 3 with symmetric nilpotent centers
Copyright policy )Polynomial Hamiltonian systems of degree 3 with symmetric nilpotent centers
We provide normal forms and the global phase portraits in the Poincaré disk for all Hamiltonian planar polynomial vector fields of degree 3 symmetric with respect to the x-axis having a nilpotent center at the origin.
Nilpotent center, General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants, Poincaré compactification, nilpotent center, 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, phase portrait, Phase portrait, Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, Polynomial Hamiltonian systems, polynomial Hamiltonian systems, Poincaré compactification
Nilpotent center, General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants, Poincaré compactification, nilpotent center, 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, phase portrait, Phase portrait, Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, Polynomial Hamiltonian systems, polynomial Hamiltonian systems, Poincaré compactification
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