Accession Number : ADA192924

Title :   Statistical Description of Stochastic Dynamics.

Descriptive Note : Final rept. 1 Jun 87-31 May 88,

Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE

Personal Author(s) : Rechester, Alexander B

PDF Url : ADA192924

Report Date : 15 May 1988

Pagination or Media Count : 5

Abstract : The main result of our research is the establishment of a general relationship for fluctuation of the spectral density of the chaotic motion which is similar to the Einstein fluctuation formula in statistical mechanics. A Gibbs-type partition of the chaotic motion is introduced. The distribution function of the spectral density defined on such partition is Gaussian. The variance of this distribution is the Fourier transform of the correlation function. This is demonstrated by direct numerical computations for the simple models of chaos. These results are the consequence of translational invariance and should be valid for the general case of chaotic motion described by differential equations.

Descriptors :   *STATISTICAL MECHANICS, *STOCHASTIC PROCESSES, COMPUTATIONS, CORRELATION, DIFFERENTIAL EQUATIONS, DISTRIBUTION FUNCTIONS, DYNAMICS, FOURIER TRANSFORMATION, FUNCTIONS(MATHEMATICS), NUMERICAL ANALYSIS, SPECTRAL ENERGY DISTRIBUTION, STATISTICS, MATHEMATICAL MODELS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE