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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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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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