Exactly solvable chaos and addition theorems of elliptic functions

Ken Umeno

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arXiv · chao-dyn/9704007

Exactly solvable chaos and addition theorems of elliptic functions

Ken Umeno

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Abstract

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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Ken Umeno. 1998-12-24. Exactly solvable chaos and addition theorems of elliptic functions. https://arxiv.org/abs/chao-dyn/9704007

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