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Article

Solutions of the Multivariate Inverse Frobenius–Perron Problem

1
Department of Physics, University of Otago, Dunedin 9016, New Zealand
2
System Manufacturing Center, National Chung-Shan Institute of Science & Technology, New Taipei City 237209, Taiwan
3
Department of Statistics, The University of Auckland, Auckland 1010, New Zealand
*
Author to whom correspondence should be addressed.
Academic Editors: José A. Tenreiro Machado, Carla M.A. Pinto, Julio Rebelo and Helena Reis
Entropy 2021, 23(7), 838; https://doi.org/10.3390/e23070838
Received: 31 May 2021 / Accepted: 18 June 2021 / Published: 30 June 2021
(This article belongs to the Special Issue Dynamical Systems, Differential Equations and Applications)
We address the inverse Frobenius–Perron problem: given a prescribed target distribution ρ, find a deterministic map M such that iterations of M tend to ρ in distribution. We show that all solutions may be written in terms of a factorization that combines the forward and inverse Rosenblatt transformations with a uniform map; that is, a map under which the uniform distribution on the d-dimensional hypercube is invariant. Indeed, every solution is equivalent to the choice of a uniform map. We motivate this factorization via one-dimensional examples, and then use the factorization to present solutions in one and two dimensions induced by a range of uniform maps. View Full-Text
Keywords: inverse Frobenius–Perron problem; Rosenblatt transformation; uniform map; multivariate probability distribution; transfer operator; ergodic map inverse Frobenius–Perron problem; Rosenblatt transformation; uniform map; multivariate probability distribution; transfer operator; ergodic map
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MDPI and ACS Style

Fox, C.; Hsiao, L.-J.; Lee, J.-E. Solutions of the Multivariate Inverse Frobenius–Perron Problem. Entropy 2021, 23, 838. https://doi.org/10.3390/e23070838

AMA Style

Fox C, Hsiao L-J, Lee J-E. Solutions of the Multivariate Inverse Frobenius–Perron Problem. Entropy. 2021; 23(7):838. https://doi.org/10.3390/e23070838

Chicago/Turabian Style

Fox, Colin, Li-Jen Hsiao, and Jeong-Eun Lee. 2021. "Solutions of the Multivariate Inverse Frobenius–Perron Problem" Entropy 23, no. 7: 838. https://doi.org/10.3390/e23070838

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