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A matrix solution to the inverse Perron-Frobenius problem

Authors: P. Góra and A. Boyarsky
Journal: Proc. Amer. Math. Soc. 118 (1993), 409-414
MSC: Primary 58F11; Secondary 28D05
MathSciNet review: 1129877
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Abstract: Let $f$ be a probability density function on the unit interval $I$. The inverse Perron-Frobenius problem involves determining a transformation $\tau :I \to I$ such that the one-dimensional dynamical system ${x_{i + 1}} = \tau ({x_i})$ has $f$ as its unique invariant density function. A matrix method is developed that provides a simple relationship between $\tau$ and $f$, where $f$ is any piecewise constant density function. The result is useful for modelling and predicting chaotic data.

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Article copyright: © Copyright 1993 American Mathematical Society