Density of orbits of semigroups of endomorphisms acting on the Adeles

Alan Haynes*, Sara Munday

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

We investigate the question of whether or not the orbit of a point in A/Q, under the natural action of a subset Sigma subset of Q, is dense in A/Q. We prove that if the set Sigma is a multiplicative semigroup Q(x) which contains at least two multiplicatively independent elements, one of which is an integer, then the orbit under Sigma alpha of any point with irrational real coordinate is dense.

Original languageEnglish
Pages (from-to)443-454
Number of pages12
JournalNew York Journal of Mathematics
Volume19
Publication statusPublished - 2013

Keywords

  • Topological dynamics
  • Adeles

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