A dynamical system linked to the sequence of prime numbers (Q2767614)
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scientific article; zbMATH DE number 1697756
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A dynamical system linked to the sequence of prime numbers |
scientific article; zbMATH DE number 1697756 |
Statements
23 October 2002
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prime numbers
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Markov map
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piecewise-linear map
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\(\sigma\)-affine fibered system
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ergodicity
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A dynamical system linked to the sequence of prime numbers (English)
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A piecewise-linear map is defined on \((0,1]\) by setting \(\phi(x)=px-1\) when \(x\in(1/p,1/q]\) for consecutive prime numbers \(p,q\). This map is studied as an example of a \(\sigma\)-affine fibered system in the sense of \textit{F. Schweiger} [Ergodic theory of fibred systems and metric number theory. Oxford, Clarendon Press (1995; Zbl 0819.11027)]. Ergodicity of an associated Markov chain is not proved, but numerical evidence is given to support its conjectured ergodicity.
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0.7208722829818726
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0.7098167538642883
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