Version 1
: Received: 23 October 2023 / Approved: 24 October 2023 / Online: 24 October 2023 (07:54:07 CEST)
How to cite:
Artés, J.C.; Llibre, J.; Vulpe, N. Dynamics of the Static Star Differential System from the Mathematical and Physical Point of Views. Preprints2023, 2023101482. https://doi.org/10.20944/preprints202310.1482.v1
Artés, J.C.; Llibre, J.; Vulpe, N. Dynamics of the Static Star Differential System from the Mathematical and Physical Point of Views. Preprints 2023, 2023101482. https://doi.org/10.20944/preprints202310.1482.v1
Artés, J.C.; Llibre, J.; Vulpe, N. Dynamics of the Static Star Differential System from the Mathematical and Physical Point of Views. Preprints2023, 2023101482. https://doi.org/10.20944/preprints202310.1482.v1
APA Style
Artés, J.C., Llibre, J., & Vulpe, N. (2023). Dynamics of the Static Star Differential System from the Mathematical and Physical Point of Views. Preprints. https://doi.org/10.20944/preprints202310.1482.v1
Chicago/Turabian Style
Artés, J.C., Jaume Llibre and Nicolae Vulpe. 2023 "Dynamics of the Static Star Differential System from the Mathematical and Physical Point of Views" Preprints. https://doi.org/10.20944/preprints202310.1482.v1
Abstract
We classify all the topologically non-equivalent phase portraits of the quadratic polynomial differential system
dx/dt = (1-2x)(y-x), dy/dt =y (2-g y-(5g-4)x/(g-1)),
in the Poincaré disc for all the values of the parameter g in R\{1}. The differential system
dx/dt = y-x, dy/dt =y (2-g y-(5g-4)x/(g-1))/(1-2x),
when the parameter g in (1,2] models the structure equations of a static star in general relativity in the case of the existence of a homologous family of solutions, being x = m(r)/r where m(r)>= 0 is the mass inside the sphere of radius r of the star, y = 4pi r^2 rho where rho is the density of the star, and t = ln (r/R) where R is the radius of the star. We classify the possible values of m(r)/r and 4pi r^2 rho when r-->0.
Keywords
Static star; polynomial vector fields; evolution
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
