Linear semigroups with coarsely dense orbits |
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Authors: | H Abels A Manoussos |
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Institution: | 1. Fakult?t für Mathematik, Universit?t Bielefeld, Postfach 100131, D-33501, Bielefeld, Germany 2. Fakult?t für Mathematik, SFB 701, Universit?t Bielefeld, Postfach 100131, D-33501, Bielefeld, Germany
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Abstract: | Let S be a finitely generated abelian semigroup of invertible linear operators on a finite-dimensional real or complex vector space V. We show that every coarsely dense orbit of S is actually dense in V. More generally, if the orbit contains a coarsely dense subset of some open cone C in V, then the closure of the orbit contains the closure of C. In the complex case the orbit is then actually dense in V. For the real case we give precise information about the possible cases for the closure of the orbit. |
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