Determinantal solutions of solvable chaotic systems

It is shown that two solvable chaotic systems, the arithmetic–harmonic mean (AHM) algorithm and the Ulam-von Neumann (UvN) 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.