Abstract
We show the existence of free dense subgroups, generated by two elements, in the holomorphic shear and overshear group of complex-Euclidean space and extend this result to the group of holomorphic automorphisms of Stein manifolds with the density property, provided there exists a generalized translation. The conjugation operator associated to this generalized translation is hypercyclic on the topological space of holomorphic automorphisms.
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Andrist, R.B., Wold, E.F. Free dense subgroups of holomorphic automorphisms. Math. Z. 280, 335–346 (2015). https://doi.org/10.1007/s00209-015-1425-8
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DOI: https://doi.org/10.1007/s00209-015-1425-8