Affiliation:
1. Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran
Abstract
In this paper, we investigate the dynamical behavior of the planar polynomial system which describes the evolution of the isotropic star. It is shown that the system has no global [Formula: see text] and no global analytic first integrals. It has an invariant algebraic curve with algebraic multiplicity [Formula: see text] and an exponential factor that comes from the multiplicity of the infinite invariant straight line. It is proved that the system can be changed into the Liénard system. By using a dominant balance analysis, we prove the system has a general solution which eventuates to a finite-time singularity. Finally, we prove the trajectories of the vector field associated with the planar system of the isotropic star do not create a trajectory manifold which means there is no pseudo-Riemannian metric [Formula: see text] in the sense of trajectory metric such that the trajectories of the isotropic star system be geodesic.
Publisher
World Scientific Pub Co Pte Lt
Subject
Physics and Astronomy (miscellaneous)
Cited by
1 articles.
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