New York Journal of Mathematics
Volume 19 (2013) 443-454


Alan Haynes and Sara Munday

Density of orbits of semigroups of endomorphisms acting on the Adeles

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Published: August 5, 2013
Keywords: Topological dynamics, Adeles
Subject: 54H20, 11J71

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


Research of both authors supported by EPSRC grant EP/J00149X/1.

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School of Mathematics, University of Bristol, Bristol, UK