Loading...
Loading...

Go to the content (press return)

Rational parameterizations approach for solving equations in some dynamical systems problems

Author
Lazaro, J. Tomás; Gasull, A.; Torregrosa, J.
Type of activity
Journal article
Journal
Qualitative theory of dynamical systems
Date of publication
2019-08
Volume
18
Number
2
First page
583
Last page
602
DOI
10.1007/s12346-018-0300-5
Repository
http://hdl.handle.net/2117/166702 Open in new window
URL
https://link.springer.com/article/10.1007%2Fs12346-018-0300-5 Open in new window
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 co...
Citation
Lazaro, J. T.; Gasull, A.; Torregrosa, J. Rational parameterizations approach for solving equations in some dynamical systems problems. "Qualitative theory of dynamical systems", Agost 2019, vol. 18, núm. 2, p. 583-602.
Keywords
Abelian integral, Bifurcation, Central configuration, Poincaré–Melnikov–Pontryagin function, Rational parameterization, Relative equilibria, Resultant
Group of research
SD - UPC Dynamical Systems

Participants