Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views

Abstract

The following differential quadratic polynomial differential system   (Formula presented.) when the parameter (Formula presented.) models the structure equations of an isotropic star having a linear barotropic equation of state, being (Formula presented.) where (Formula presented.) is the mass inside the sphere of radius r of the star, (Formula presented.) where (Formula presented.) is the density of the star, and (Formula presented.) 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 (Formula presented.). Second, using the information of the different phase portraits obtained we classify the possible limit values of (Formula presented.) and (Formula presented.) of an isotropic star when r decreases.