Academic Journal
Rational Parameterizations Approach for Solving Equations in Some Dynamical Systems Problems
| Title: | Rational Parameterizations Approach for Solving Equations in Some Dynamical Systems Problems |
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| Authors: | Armengol Gasull, J. Tomás Lázaro, Joan Torregrosa |
| Contributors: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC |
| Source: | Recercat. Dipósit de la Recerca de Catalunya instname UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona Recercat: Dipósit de la Recerca de Catalunya Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Publisher Information: | Springer Science and Business Media LLC, 2018. |
| Publication Year: | 2018 |
| Subject Terms: | Differential equations, 34 Ordinary differential equations::34C Qualitative theory [Classificació AMS], Classificació AMS::34 Ordinary differential equations::34C Qualitative theory, Equacions diferencials, 01 natural sciences, Àlgebra commutativa, Rational parameterization, Resultant, 14 Algebraic geometry::14E Birational geometry [Classificació AMS], 0101 mathematics, Relative equilibria, Àrees temàtiques de la UPC::Matemàtiques i estadística, 13 Commutative rings and algebras::13P Computational aspects of commutative algebra [Classificació AMS], Abelian integral, Poincaré-Melnikov-Pontryagin function, Matemàtiques i estadística [Àrees temàtiques de la UPC], Classificació AMS::14 Algebraic geometry::14E Birational geometry, Central configuration, Classificació AMS::13 Commutative rings and algebras::13P Computational aspects of commutative algebra, Poincaré–Melnikov–Pontryagin function, Classificació AMS::37 Dynamical systems and ergodic theory::37N Applications, Bifurcation, Commutative algebra, 37 Dynamical systems and ergodic theory::37N Applications [Classificació AMS], Central configuration |
| Description: | 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. |
| Document Type: | Article |
| File Description: | application/pdf |
| Language: | English |
| ISSN: | 1662-3592 1575-5460 |
| DOI: | 10.1007/s12346-018-0300-5 |
| Access URL: | https://ddd.uab.cat/pub/artpub/2019/221348/GasLazTor2018.pdf http://hdl.handle.net/2072/439782 https://ddd.uab.cat/record/221348 http://hdl.handle.net/2117/166702 https://upcommons.upc.edu/handle/2117/166702 https://dialnet.unirioja.es/servlet/articulo?codigo=7676883 https://link.springer.com/article/10.1007/s12346-018-0300-5 https://hdl.handle.net/2117/166702 https://doi.org/10.1007/s12346-018-0300-5 |
| Rights: | Springer TDM CC 0 CC BY NC ND URL: http://rightsstatements.org/vocab/InC/1.0/ |
| Accession Number: | edsair.doi.dedup.....a76c0a29a8d0fe67d54c9128f27c19b5 |
| Database: | OpenAIRE |
| ISSN: | 16623592 15755460 |
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| DOI: | 10.1007/s12346-018-0300-5 |