On the stochasticity in relativistic cosmology

I. M. Khalatnikov; E. M. Lifshitz; K. M. Khanin; L. N. Shchur; Ya G. Sinai

doi:10.1007/BF01017851

On the stochasticity in relativistic cosmology

I. M. Khalatnikov, E. M. Lifshitz, K. M. Khanin, L. N. Shchur, Ya G. Sinai

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116 Scopus citations

Abstract

It was shown earlier by I. M. Lifshitz and two of us that the evolution of the relativistic cosmological models towards the singularity undergoes spontaneous stochastization.⁽¹⁾ In the present paper it is shown that the statistical parameters of this evolution can be calculated in an exact manner. From the point of view of the general ergodic theory we deal here with a specific mode of stochastization of a deterministic dynamical system with a five-dimensional phase space. The knowledge of the source of stochasticity makes it possible to develop a quantitative statistical theory with appreciable completeness.

Original language	English (US)
Pages (from-to)	97-114
Number of pages	18
Journal	Journal of Statistical Physics
Volume	38
Issue number	1-2
DOIs	https://doi.org/10.1007/BF01017851
State	Published - Jan 1985

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Stochastization
cosmological models
singularity

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10.1007/BF01017851

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title = "On the stochasticity in relativistic cosmology",

abstract = "It was shown earlier by I. M. Lifshitz and two of us that the evolution of the relativistic cosmological models towards the singularity undergoes spontaneous stochastization.(1) In the present paper it is shown that the statistical parameters of this evolution can be calculated in an exact manner. From the point of view of the general ergodic theory we deal here with a specific mode of stochastization of a deterministic dynamical system with a five-dimensional phase space. The knowledge of the source of stochasticity makes it possible to develop a quantitative statistical theory with appreciable completeness.",

keywords = "Stochastization, cosmological models, singularity",

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year = "1985",

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doi = "10.1007/BF01017851",

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AU - Khalatnikov, I. M.

AU - Lifshitz, E. M.

AU - Khanin, K. M.

AU - Shchur, L. N.

AU - Sinai, Ya G.

PY - 1985/1

Y1 - 1985/1

N2 - It was shown earlier by I. M. Lifshitz and two of us that the evolution of the relativistic cosmological models towards the singularity undergoes spontaneous stochastization.(1) In the present paper it is shown that the statistical parameters of this evolution can be calculated in an exact manner. From the point of view of the general ergodic theory we deal here with a specific mode of stochastization of a deterministic dynamical system with a five-dimensional phase space. The knowledge of the source of stochasticity makes it possible to develop a quantitative statistical theory with appreciable completeness.

AB - It was shown earlier by I. M. Lifshitz and two of us that the evolution of the relativistic cosmological models towards the singularity undergoes spontaneous stochastization.(1) In the present paper it is shown that the statistical parameters of this evolution can be calculated in an exact manner. From the point of view of the general ergodic theory we deal here with a specific mode of stochastization of a deterministic dynamical system with a five-dimensional phase space. The knowledge of the source of stochasticity makes it possible to develop a quantitative statistical theory with appreciable completeness.

KW - Stochastization

KW - cosmological models

KW - singularity

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EP - 114

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 1-2

ER -

On the stochasticity in relativistic cosmology

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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