Higher-dimensional homogeneous cosmological models as autonomous dynamical systems

1991 ◽  
Vol 23 (2) ◽  
pp. 189-207 ◽  
Author(s):  
M. Heusler
Keyword(s):  
Dynamical Systems ◽  
Cosmological Models ◽  
Homogeneous Cosmological Models ◽  
Higher Dimensional ◽  
Autonomous Dynamical Systems

Hypersurface-homogeneous cosmological models with dynamical equation of state parameter in Lyra geometry

2015 ◽  
Vol 93 (10) ◽  
pp. 1100-1105 ◽  
Author(s):  
Shri Ram ◽  
S. Chandel ◽  
M.K. Verma
Keyword(s):  
Dynamical Equation ◽  
State Parameter ◽  
Lyra Geometry ◽  
Cosmological Models ◽  
Anisotropic Fluid ◽  
Late Time ◽  
Field Equations ◽  
Homogeneous Cosmological Models ◽  
Negative Constant ◽  
Equation Of State Parameter

The hypersurface homogeneous cosmological models are investigated in the presence of an anisotropic fluid in the framework of Lyra geometry. Exact solutions of field equations are obtained by applying a special law of variation for mean Hubble parameter that gives a negative constant value of the deceleration parameter. These solutions correspond to anisotropic accelerated expanding cosmological models that isotropize for late time even in the presence of anisotropic fluid. The anisotropy of the fluid also isotropizes at late time. Some physical and kinematical properties of the model are also discussed.

HIGHER-DIMENSIONAL COSMOLOGICAL MODELS WITH STRANGE QUARK MATTER

2006 ◽  
Vol 15 (04) ◽  
pp. 477-483 ◽  
Author(s):  
IHSAN YILMAZ ◽  
ATTILA ALTAY YAVUZ
Keyword(s):  
General Relativity ◽  
Quark Gluon Plasma ◽  
Quark Matter ◽  
Strange Quark ◽  
Gluon Plasma ◽  
Strange Quark Matter ◽  
Cosmological Models ◽  
Field Equations ◽  
Higher Dimensional ◽  
Different Types

In this article, we study higher-dimensional cosmological models with quark–gluon plasma in the context of general relativity. For this purpose, we consider quark–gluon plasma as a perfect fluid in the higher-dimensional universes. After solving Einstein's field equations, we have analyzed this matter for the different types of universes in the higher- and four-dimensional universes. Also, we have discussed the features of obtained solutions.

scholarly journals State space decomposition for non-autonomous dynamical systems

2011 ◽  
Vol 141 (5) ◽  
pp. 957-974 ◽  
Author(s):  
Xiaopeng Chen ◽  
Jinqiao Duan
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
State Space ◽  
Decomposition Theorem ◽  
Navier Stokes ◽  
Locally Compact ◽  
Infinite Dimensional ◽  
The Lorenz System ◽  
A Chain ◽  
Autonomous Dynamical Systems

The decomposition of state spaces into dynamically different components is helpful for understanding dynamics of complex systems. A Conley-type decomposition theorem is proved for non-autonomous dynamical systems defined on a non-compact but separable state space. Specifically, the state space can be decomposed into a chain-recurrent part and a gradient-like part. This result applies to both non-autonomous ordinary differential equations on a Euclidean space (which is only locally compact), and to non-autonomous partial differential equations on an infinite-dimensional function space (which is not even locally compact). This decomposition result is demonstrated by discussing a few concrete examples, such as the Lorenz system and the Navier–Stokes system, under time-dependent forcing.

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