Abstract
In this paper, we bring together results about the existence of a somewhere dense (resp. dense) orbit and the minimal number of generators for abelian semigroups of matrices on Rn. We solve the problem of determining the minimal number of matrices in normal form over R which form a hypercyclic abelian semigroup on Rn. In particular, we show that no abelian semigroup generated by [n+12] matrices on Rn can be hypercyclic ([] denotes the integer part).
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