In this paper, we give a review of the Inverse Frobenius–Perron problem (IFPP): how to create\udchaotic maps with desired invariant densities. After describing some existing methods for solving\udthe IFPP, we present a new and simple matrix method of doing this. We show how the invariant\uddensity and the autocorrelation properties of the maps can be controlled independently. We\udalso give some fundamental results on switching between a number of different chaotic maps\udand the effect this has on the overall invariant density of the system. The invariant density of\udthe switched system can be controlled by varying the probabilities of choosing each individual\udmap. Finally, we present an interesting application of the matrix method to image generation,\udby synthesizing a two-dimensional map, which when iterated, generates a well-known image.
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