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Parry–Daniels map : ウィキペディア英語版
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.
It is named after the English mathematician Bill Parry and the British statistician Henry Daniels, who independently studied the map in papers published in 1962.
==Definition==

Given an integer ''n'' ≥ 1, let Σ denote the ''n''-dimensional simplex in R''n''+1 given by
:\Sigma := \ | 0 \leq x_i \leq 1 \mbox i \mbox x_0 + x_1 + \dots + x_n = 1 \}.
Let ''π'' be a permutation such that
:x_ \leq x_ \leq \dots \leq x_.
Then the Parry–Daniels map
: T_ : \Sigma \to \Sigma
is defined by
:T_\pi (x_0, x_1, \dots, x_n) := \left( \frac} , \frac} - x_}{x_{\pi (n)}} \right).


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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