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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Bibliographic Details
Published in:Qualitative theory of dynamical systems Vol. 18; no. 2; pp. 583 - 602
Main Authors: Gasull, Armengol, Lázaro, J. Tomás, Torregrosa, Joan
Format: Journal Article Publication
Language:English
Published: Cham Springer International Publishing 01.08.2019
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-018-0300-5