Differential equations, Computational aspects of algebraic curves, :34 Ordinary differential equations::34C Qualitative theory [Classificació AMS], Classificació AMS::34 Ordinary differential equations::34C Qualitative theory, Dynamical systems in classical and celestial mechanics, Equacions diferencials, Àlgebra commutativa, Rational parameterization, Resultant, :14 Algebraic geometry::14E Birational geometry [Classificació AMS], Relative equilibria, Bifurcation theory for ordinary differential equations, Àrees temàtiques de la UPC::Matemàtiques i estadística, Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.), :13 Commutative rings and algebras::13P Computational aspects of commutative algebra [Classificació AMS], Abelian integral, Poincaré-Melnikov-Pontryagin function, :Matemàtiques i estadística [Àrees temàtiques de la UPC], relative equilibria, Classificació AMS::14 Algebraic geometry::14E Birational geometry, Central configuration, Classificació AMS::13 Commutative rings and algebras::13P Computational aspects of commutative algebra, rational parameterization, Solving polynomial systems; resultants, bifurcation, Poincaré–Melnikov–Pontryagin function, Classificació AMS::37 Dynamical systems and ergodic theory::37N Applications, Bifurcation, Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics, abelian integral, Commutative algebra, :37 Dynamical systems and ergodic theory::37N Applications [Classificació AMS], central configuration, Central configuration, resultant