Determinantal solutions of solvable chaotic systems

[摘要] 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. (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2002-08-15

[关键词] solvable chaotic system;determinantal solution;additional formula;Riccati difference equation;Chebyshev polynomial