Density of orbits of semigroups of endomorphisms acting on the Adeles

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… CONTINUE READING