Exactly solvable chaos and addition theorems of elliptic functions
chao-dyn
2008-02-03 v3 Chaotic Dynamics
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.
Keywords
Cite
@article{arxiv.chao-dyn/9704007,
title = {Exactly solvable chaos and addition theorems of elliptic functions},
author = {Ken Umeno},
journal= {arXiv preprint arXiv:chao-dyn/9704007},
year = {2008}
}
Comments
14 pages, Latex. typos corrected, comments related to permutable rational functions of J.F. Ritt added