Affiliation:
1. Department of Mathematics, Universitat Autònoma de Barcelona, Bellaterra, 08193 Barcelona, Spain
2. Vladimir Andrunakievichi Institute of Mathematics and Computer Science, MD-2028 Chisinau, Moldova
Abstract
The following differential quadratic polynomial differential system dxdt=y−x, dydt=2y−yγ−12−γy−5γ−4γ−1x, when the parameter γ∈(1,2] models the structure equations of an isotropic star having a linear barotropic equation of state, being x=m(r)/r where m(r)≥0 is the mass inside the sphere of radius r of the star, y=4πr2ρ where ρ is the density of the star, and t=ln(r/R) where R is the radius of the star. First, we classify all the topologically non-equivalent phase portraits in the Poincaré disc of these quadratic polynomial differential systems for all values of the parameter γ∈R∖{1}. Second, using the information of the different phase portraits obtained we classify the possible limit values of m(r)/r and 4πr2ρ of an isotropic star when r decreases.
Funder
Agencia Estatal de Investigación
H2020 European Research Council
AGAUR
Acadèmia de Ciències i Arts de Barcelona