TY - JOUR
T1 - Rational Parameterizations Approach for Solving Equations in Some Dynamical Systems Problems
AU - Gasull, Armengol
AU - Lázaro, J. Tomás
AU - Torregrosa, Joan
PY - 2019/8/1
Y1 - 2019/8/1
N2 - © 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.
AB - © 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.
KW - Poincaré–Melnikov–Pontryagin function
KW - Central configuration
KW - Relative equilibria
KW - Resultant
KW - Abelian integral
KW - Rational parameterization
KW - Bifurcation
UR - http://www.mendeley.com/research/rational-parameterizations-approach-solving-equations-some-dynamical-systems-problems
UR - https://dialnet.unirioja.es/servlet/articulo?codigo=7676883
UR - https://www.scopus.com/pages/publications/85064249598
U2 - 10.1007/s12346-018-0300-5
DO - 10.1007/s12346-018-0300-5
M3 - Article
SN - 1575-5460
VL - 18
SP - 583
EP - 602
JO - Qualitative Theory of Dynamical Systems
JF - Qualitative Theory of Dynamical Systems
ER -