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Parry–Daniels map

Mathematical function related to dynamical systems From Wikipedia, the free encyclopedia

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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.

Definition

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Perspective

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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References

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