Free dense subgroups of holomorphic automorphisms

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.

(Table 1) Chemical composition of Mediterranean halite from DSDP Hole 13-134

Bromine content of a 15 cm halite core from Deep Sea Drilling Project Leg XIII Hole 134 was analyzed at 1.5 cm intervals. The Br varies from 140 to 254 ppm, and three maxima were found to coincide with three postulated horizons of desiccation. The Br profile confirms the interpretation from sedimentologic evidence that Mediterranean salts were deposited in a desiccating basin.