Topological classification of some SD Hamiltonian systems

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Cites Work

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Classification of global phase portraits and bifurcation diagrams of Hamiltonian systems with rational potential
Bifurcation diagrams for Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields
Global phase portrait of a degenerate Bogdanov-Takens system with symmetry
Phase portraits of separable Hamiltonian systems
Bifurcation at infinity in polynomial vector fields
Classification of global phase portraits of planar quartic quasi-homogeneous polynomial differential systems
The classification on the global phase portraits of two-dimensional Lotka-Volterra system
Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3
Quadratic Hamiltonian vector fields
Phase portrait of Hamiltonian systems with homogeneous nonlinearities
Global dynamics of a SD oscillator
Linear type centers of polynomial Hamiltonian systems with nonlinearities of degree 4 symmetric with respect to the \(\mathrm{y}\)-axis
\(Z_2\)-equivariant linear type bi-center cubic polynomial Hamiltonian vector fields
Phase portraits and bifurcation diagram of the Gray-Scott model
Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields
Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields
Qualitative theory of planar differential systems
Dynamical analysis of a cubic Liénard system with global parameters (II)
Algebraic Particular Integrals, Integrability and the Problem of the Center
Dynamical analysis of a cubic Liénard system with global parameters
Classification of Continuous Flows on 2-Manifolds
Bifurcation Diagrams and Global Phase Portraits for Some Hamiltonian Systems with Rational Potentials
A SURVEY ON THE BLOW UP TECHNIQUE
Global Structure of Ordinary Differential Equations in the Plane

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