We investigate the question of whether or not the orbit of a point in A/Q,
under the natural action of a subset S of Q, is dense in A/Q. We prove that if
the set S is a multiplicative semigroup which contains at least two
multiplicatively independent elements, one of which is an integer, then the
orbit under S of any point with irrational real coordinate is dense.Comment: 13 page

Haynes, Alan

Munday, Sara

English

arXiv

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.</p

Density of orbits of semigroups of endomorphisms acting on the Adeles

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