Treffer: A dynamical system linked to the sequence of prime numbers

Title:
A dynamical system linked to the sequence of prime numbers
Authors:
Costé, Alain
Publisher Information:
Académie des Sciences, Paris; Elsevier, Paris
Subject Terms:
Markov map, piecewise-linear map, prime numbers, ergodicity, Relations of ergodic theory with number theory and harmonic analysis, \(\sigma\)-affine fibered system, Low-dimensional dynamical systems, Primes
Document Type:
Fachzeitschrift Article
File Description:
application/xml
DOI:
10.1016/s0764-4442(01)02099-7
Access URL:
https://zbmath.org/1697756
Accession Number:
edsair.c2b0b933574d..f021c6e5d6b9fa6d3b674e3015d95d90
Database:
OpenAIRE

Weitere Informationen

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.