Exactly solvable chaos and addition theorems of elliptic functions
Abstract
Description
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.
14 pages, Latex. typos corrected, comments related to permutable rational functions of J.F. Ritt added
14 pages, Latex. typos corrected, comments related to permutable rational functions of J.F. Ritt added