
Contents
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66. Goals 66. Goals
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67. Definitions of Variables and Distribution Functions 67. Definitions of Variables and Distribution Functions
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68. BBGKY Hierarchy Equations 68. BBGKY Hierarchy Equations
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69. Fluid Limit 69. Fluid Limit
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70. Evolution of the Integral of ξ 70. Evolution of the Integral of ξ
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71. Particle Conservation Equations 71. Particle Conservation Equations
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A. Conservation of pairs A. Conservation of pairs
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B. Conservation of triplets and quadruplets B. Conservation of triplets and quadruplets
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72. Relative Peculiar Velocity Dispersion 72. Relative Peculiar Velocity Dispersion
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73. Similarity Solution 73. Similarity Solution
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A. Scale-invariant solution A. Scale-invariant solution
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B. Nonlinear limit B. Nonlinear limit
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74. Cosmic Energy Equation 74. Cosmic Energy Equation
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75. Cosmic Virial Theorem 75. Cosmic Virial Theorem
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76. Joint Distribution in Redshift and Position 76. Joint Distribution in Redshift and Position
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A. Two-Point correlation function in redshift space A. Two-Point correlation function in redshift space
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B. Models for ξυ B. Models for ξυ
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C. Peculiar velocities and the mean mass density C. Peculiar velocities and the mean mass density
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77. Behavior of the Halo Around a Cluster of Galaxies 77. Behavior of the Halo Around a Cluster of Galaxies
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A. The mean halo of an abell cluster A. The mean halo of an abell cluster
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B. Statistical dynamics B. Statistical dynamics
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C. Stability condition C. Stability condition
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D. Streaming motion at targe r D. Streaming motion at targe r
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78. Superclusters 78. Superclusters
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79. Problems and Prospects 79. Problems and Prospects
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IV. Dynamics and Statistics
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Published:September 2020
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Abstract
This chapter studies how the n-point correlation functions have proved useful not only as descriptive statistics but also as dynamic variables in the Newtonian theory of the evolution of clustering. It generalizes the functions to mass correlation functions in position and momentum, and derives the BBGKY hierarchy of equations for their evolution. This yields a new way to analyze the evolution of mass clustering in an expanding universe. Of course, the main interest in the approach comes from the thought that the observed galaxy correlation functions may yield useful approximations to the mass correlation functions, so the observations may provide boundary values for the dynamical theory of evolution of the mass correlation functions. The test will be whether one can find a consistent theory for the joint distributions in galaxy positions and velocities.
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