Density of orbits of semigroups of endomorphisms acting on the Adeles

Alan Haynes; Sara Munday

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arXiv · 1303.1661

Density of orbits of semigroups of endomorphisms acting on the Adeles

Alan Haynes·Sara Munday

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Abstract

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.

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Alan Haynes, Sara Munday. 2013-03-07. Density of orbits of semigroups of endomorphisms acting on the Adeles. https://arxiv.org/abs/1303.1661

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