Exactly solvable chaos and addition theorems of elliptic functions

Details Exactly solvable chaos and addition theorems of elliptic functions Exactly solvable chaos and addition theorems of elliptic functions

1997-04-04

arxiv.org/abs/chao-dyn/9704007v3

RIMS Kokyuroku No. 1098 (1999),pp.104-117.

Nonlinear Sciences

Chaotic Dynamics

14 pages, Latex. typos corrected, comments related to permutable rational functions of J.F. Ritt added

Scientific paper

A unified view is given to recent developments about a systematic method of constructing rational mappings as ergodic transformations with non-uniform invariant measures on the unit interval I=[0,1]. All of the rational ergodic mappings of I with explicit non-uniform invariant densities can be obtained by addition theorems of elliptic functions. It is shown here that the class of the rational ergodic mappings I->I are essentially same as the permutable rational functions obtained by J. F. Ritt.

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