Synthesizing Chaotic Maps with Prescribed Invariant Densities
Rogers, Alan and Shorten, Robert and Heffernan, Daniel M. (2004) Synthesizing Chaotic Maps with Prescribed Invariant Densities. Physics Letters A, 330 (6). pp. 435-441.
The Inverse Frobenius-Perron problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this note, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized.
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