Abstract
In this paper we prove several results on approximation of biholomorphic mappings between domains in C" (n _>-2) by holomorphic automorphisms of C". Recall that the group of holomorphic automorphisms of C", denoted Aut C", consists of those holomorphic mappings ~ : C "--, C" that have a holomorphic inverse 4 1 : C" --* C". With the topology of uniform convergence on compact sets, Aut C" is a topological group. While the group Aut C 1 of automorphisms of the complex plane consists only of the linear mappings az + b (a, b e C, a 4= 0), the group Aut C" is very large and complicated when n > 2. Let us choose a linear coordinate system on C" and write the coordinates as z = (z ' ,w), where Z'~-(Z1, . . . ,Zn_I)C--C n 1 and w = z ,~ C. Then AutC n contains mappings of the form
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