Rational parameterizations approach for solving equations in some dynamical systems problems
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Lázaro, J. Tomás (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2019
Abstract:	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.
Grants:	Ministerio de Economía y Competitividad MTM2015-65715-P Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1049 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Bifurcation ; Resultant ; Rational parameterization ; Abelian integral ; Poincaré-Melnikov-Pontryagin function ; Relative equilibria ; Central configuration
Published in:	Qualitative theory of dynamical systems, Vol. 18, Issue 2 (August 2019) , p. 583-602, ISSN 1662-3592

DOI: 10.1007/s12346-018-0300-5

Postprint 16 p, 431.6 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles