Rational Parameterizations Approach for Solving Equations in Some Dynamical Systems Problems

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 dyna...

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Podrobná bibliografie
Vydáno v:	Qualitative theory of dynamical systems Ročník 18; číslo 2; s. 583 - 602
Hlavní autoři:	Gasull, Armengol, Lázaro, J. Tomás, Torregrosa, Joan
Médium:	Journal Article Publikace
Jazyk:	angličtina
Vydáno:	Cham Springer International Publishing 01.08.2019 Springer Nature B.V
Témata:	13 Commutative rings and algebras 13P Computational aspects of commutative algebra 14 Algebraic geometry 14E Birational geometry 34 Ordinary differential equations 34C Qualitative theory 37 Dynamical systems and ergodic theory 37N Applications Abelian integral Bifurcation Celestial mechanics Central configuration Classificació AMS Commutative algebra Difference and Functional Equations Differential equations Dynamical systems Dynamical Systems and Ergodic Theory Equacions diferencials Matemàtiques i estadística Mathematics Mathematics and Statistics Poincaré–Melnikov–Pontryagin function Polynomials Rational parameterization Relative equilibria Resultant Àlgebra commutativa Àrees temàtiques de la UPC Poincaré–Melnikov–Pontryagin function Central configuration Resultant Relative equilibria Rational parameterization Abelian integral Primary: 34C23 37N05 Bifurcation 14E05 34C08 Secondary: 13P15
ISSN:	1575-5460, 1662-3592
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Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1575-5460 1662-3592
DOI:	10.1007/s12346-018-0300-5