Characterizing chaotic processes that generate uniform invariant density

Universal formulations for four types of discrete chaotic processes that generate (preserve) uniform invariant density are provided. Characterizations such as necessary and/or sufficient conditions are established. It is revealed that such processes are “invariant” with branch-mirroring and horizontal mirroring. In addition, horizontally linear combinations of such processes remain to be in the same family. Theoretical findings are well verified by the computer simulations.