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Determinantal solutions of solvable chaotic systems. (English) Zbl 1008.65095

Authors’ abstract: It is shown that two solvable chaotic systems, the arithmetic-harmonic mean algorithm and the Ulam-von Neumann 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.

MSC:

65P20 Numerical chaos
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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