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| In [[mathematics]], the '''Parry–Daniels map''' is a [[function (mathematics)|function]] studied in the context of [[dynamical systems]]. Typical questions concern the existence of an [[invariant measure|invariant]] or [[ergodic (adjective)|ergodic measure]] for the map.
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| It is named after the [[England|English]] [[mathematician]] [[Bill Parry (mathematician)|Bill Parry]] and the [[UK|British]] [[statistician]] [[Henry Daniels]], who independently studied the map in papers published in 1962.
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| ==Definition==
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| Given an [[integer]] ''n'' ≥ 1, let Σ denote the ''n''-[[dimension]]al [[simplex]] in '''R'''<sup>''n''+1</sup> given by
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| :<math>\Sigma := \{ x = (x_0, x_1, \dots, x_n) \in \mathbb{R}^{n + 1} | 0 \leq x_i \leq 1 \mbox{ for each } i \mbox{ and } x_0 + x_1 + \dots + x_n = 1 \}.</math>
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| Let ''π'' be a [[permutation]] such that
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| :<math>x_{\pi(0)} \leq x_{\pi (1)} \leq \dots \leq x_{\pi (n)}.</math> | |
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| Then the '''Parry–Daniels map'''
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| : <math>T_{\pi} : \Sigma \to \Sigma</math> | |
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| is defined by
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| :<math>T_\pi (x_0, x_1, \dots, x_n) := \left( \frac{x_{\pi (0)}}{x_{\pi (n)}} , \frac{x_{\pi (1)} - x_{\pi (0)}}{x_{\pi (n)}}, \dots, \frac{x_{\pi (n)} - x_{\pi (n - 1)}}{x_{\pi (n)}} \right).</math>
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| {{DEFAULTSORT:Parry-Daniels map}}
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| [[Category:Dynamical systems]]
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| {{mathanalysis-stub}}
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Latest revision as of 15:59, 18 September 2014
Nice to meet you, my title is Refugia. What I love performing is to collect badges but I've been using on new issues lately. For years I've been working as a payroll clerk. Her family lives in Minnesota.
Here is my web site; http://www.gaysphere.net/user/KJGI