Inverse Problem and Central Limit Theorem in Chaotic Map Theory.

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  • Sogo Kiyoshi
    Department of Physics, School of Science, Kitasato University, 1–15–1 Kitasato, Sagamihara, Kanagawa 228–0829

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An inverse problem to find chaotic map(s) having a given invariant measure is formulated using a functional equation. A set of exact solutions, termed the Chebyshev hierarchy (maps defined by Chebyshev polynomials), is found for this equation. Then, an analogue of the central limit theorem is formulated and is exemplified by the Chebyshev hierarchy through explicit calculations.

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