document: Determinantal solutions of solvable chaotic systems It is shown that two solvable chaotic systems , the arithmetic-harmonic mean -LRB- ARM -RRB- algorithm and the Ulam-von Neumann -LRB- UvN -RRB- map , have determinantal solutions . An additional formula for certain determinants and Riccati difference equations play a key role in both cases . Two infinite hierarchies of solvable chaotic systems are presented which have determinantal solutions
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