© 2018, Springer Nature Switzerland AG. We show how the use of rational parameterizations facilitates the study of the number of solutions of many systems of equations involving polynomials and square roots of polynomials. We illustrate the effectiveness of this approach, applying it to several problems appearing in the study of some dynamical systems. Our examples include Abelian integrals, Melnikov functions and a couple of questions in Celestial Mechanics: the computation of some relative equilibria and the study of some central configurations.
- Abelian integral
- Central configuration
- Poincaré–Melnikov–Pontryagin function
- Rational parameterization
- Relative equilibria