# Linear semigroups with coarsely dense orbits

Abels H, Manoussos A (2014)
Israel Journal of Mathematics 200(1): 327-341.

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Let $S$ be a finitely generated abelian semigroup of invertible linearoperators on a finite dimensional vector space $V$. We show that every coarselydense orbit of $S$ is actually dense in $V$. More generally, if the orbitcontains a coarsely dense subset of some open cone $C$ in $V$ then the closureof the orbit contains the closure of $C$. In the complex case the orbit is thenactually dense in $V$. For the real case we give precise information about thepossible cases for the closure of the orbit.
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Abels H, Manoussos A. Linear semigroups with coarsely dense orbits. Israel Journal of Mathematics. 2014;200(1):327-341.
Abels, H., & Manoussos, A. (2014). Linear semigroups with coarsely dense orbits. Israel Journal of Mathematics, 200(1), 327-341. doi:10.1007/s11856-014-0020-8
Abels, H., and Manoussos, A. (2014). Linear semigroups with coarsely dense orbits. Israel Journal of Mathematics 200, 327-341.
Abels, H., & Manoussos, A., 2014. Linear semigroups with coarsely dense orbits. Israel Journal of Mathematics, 200(1), p 327-341.
H. Abels and A. Manoussos, “Linear semigroups with coarsely dense orbits”, Israel Journal of Mathematics, vol. 200, 2014, pp. 327-341.
Abels, H., Manoussos, A.: Linear semigroups with coarsely dense orbits. Israel Journal of Mathematics. 200, 327-341 (2014).
Abels, Herbert, and Manoussos, Antonios. “Linear semigroups with coarsely dense orbits”. Israel Journal of Mathematics 200.1 (2014): 327-341.
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arXiv 1108.2221