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.
Definition
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
References
- Zweimüller, Roland. "Surrey Notes on Infinite Ergodic Theory" (PDF).
- Parry, William (1962). "Ergodic Properties of Some Permutation Processes". Biometrika. 49 (1/2): 151–154. doi:10.2307/2333475. ISSN 0006-3444. JSTOR 2333475.
- Daniels, H. E. (1962). "Processes Generating Permutation Expansions". Biometrika. 49 (1/2): 139–149. doi:10.2307/2333474. ISSN 0006-3444. JSTOR 2333474.
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