Parry–Daniels map

In mathematics, the Parry–Daniels map is a function studied in the context of dynamical systems.

Typical questions concern the existence of an invariant or ergodic measure for the map.

[1] It is named after the English mathematician Bill Parry[2] and the British statistician Henry Daniels,[3] who independently studied the map in papers published in 1962.

Given an integer n ≥ 1, let Σ denote the n-dimensional simplex in Rn+1 given by Let π be a permutation such that Then the Parry–Daniels map is defined by

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