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Anikin V. M., Arkadaksky S. S., Remizov A. S., Kuptsov S. N., Vasilenko L. P. Investigation of structure of invariant density for Renyi map by Gauss method. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 6, pp. 46-56. DOI: 10.18500/0869-6632-2008-16-6-46-56

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Investigation of structure of invariant density for Renyi map by Gauss method

Anikin Valerij Mihajlovich, Saratov State University
Arkadaksky Sergej Sergeevich, Saratov State University
Remizov Aleksandr Sergeevich, Saratov State University
Kuptsov Sergej Nikolaevich, Saratov State University
Vasilenko Leonid Petrovich, Saratov State University

It is shown that the structure of the invariant density for Renyi map xn+1 = = βxn mod 1, (1 < β < 2) may be clarified by action of the Perron–Frobenius operator on the uniform distribution. The invariant density is presented by finite linear combination of characteristic functions defined on the unit interval according to special rule. Some algebraic equations with entire coefficients are formulated for parameter β corresponding values definition.

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