Fox Colin, Hsiao Li-Jen, Lee Jeong-Eun Kate
Department of Physics, University of Otago, Dunedin 9016, New Zealand.
System Manufacturing Center, National Chung-Shan Institute of Science & Technology, New Taipei City 237209, Taiwan.
Entropy (Basel). 2021 Jun 30;23(7):838. doi: 10.3390/e23070838.
We address the inverse Frobenius-Perron problem: given a prescribed target distribution ρ, find a deterministic map such that iterations of 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 -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.
