TY - JOUR
T1 - Compact invariant sets of the static spherically symmetric Einstein-Yang-Mills equations
AU - Starkov, Konstantin E.
PY - 2010/4/5
Y1 - 2010/4/5
N2 - In this Letter we obtain results concerning compact invariant sets of the static spherically symmetric Einstein-Yang-Mills (EYM) equations with help of studies of its localization. Let a be a cosmological constant and s be another parameter entering into these equations which is used for considering the physical time as a temporal variable, with s = 1, while s = - 1 is used for considering the physical time as a spatial variable. We show that in case s = 1; a < 0 the location of any compact invariant set is described by some system of linear inequalities. Then we prove that in case s = 1; a > 0 the set of all compact invariant sets consists of two equilibrium points only. Further, we state that in cases s = - 1; a < 0 and s = - 1; a > 0 there are only two equilibrium points and there are no periodic orbits. In addition, we prove that in the last two cases there are neither homoclinic orbits nor heteroclinic orbits as well.
AB - In this Letter we obtain results concerning compact invariant sets of the static spherically symmetric Einstein-Yang-Mills (EYM) equations with help of studies of its localization. Let a be a cosmological constant and s be another parameter entering into these equations which is used for considering the physical time as a temporal variable, with s = 1, while s = - 1 is used for considering the physical time as a spatial variable. We show that in case s = 1; a < 0 the location of any compact invariant set is described by some system of linear inequalities. Then we prove that in case s = 1; a > 0 the set of all compact invariant sets consists of two equilibrium points only. Further, we state that in cases s = - 1; a < 0 and s = - 1; a > 0 there are only two equilibrium points and there are no periodic orbits. In addition, we prove that in the last two cases there are neither homoclinic orbits nor heteroclinic orbits as well.
UR - http://www.scopus.com/inward/record.url?scp=77949338653&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2010.02.035
DO - 10.1016/j.physleta.2010.02.035
M3 - Artículo
SN - 0375-9601
VL - 374
SP - 1728
EP - 1731
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 15-16
ER -