Inverse and Ordinary Eigenvalue Problems in Frobenius-Perron Equation(General)
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概要
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We deal with exactly solvable inverse problems of finding 1D mappings from knowledge of given invariant densities and eigenfunctions in 1D Frobenius-Perron equations, and we find the 1D mappings yielding the white Gaussian densiy and the white Lorentzian densiy. We also find the exact eigenvalues for the quadratic eigenfunction. In the latter part, we construct the approximate ortho-normal set of eigenfunctions for a given n-D mapping either of invertible type or of noninvertible type on the basis of the Markov chain assumption. We find the distributions of the eigenvalues in the complex plane, and the theoretical formulas for the spectral decomposition of the correlation by utilizing the weighted sum of delta functions and the weighted sum of auxiliary functions.
- 社団法人日本物理学会の論文
- 2006-11-15
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