Volume-preserving automorphisms of <b>C</b>⊃n⊃

Abstract

Let Aut1(C n ) be the group of all automorphisms F of Cn with Jacobian J(F) equal to 1. A shear is a map of type where f is independent of zn and Gn is the subgroup of Aut1 (C n )consisting of all finite compositions of shears. We prove THEOREM A . THLOREM B G 2 is a proper subgroup of Aut1(C 2). In particular, the map of C 2 is not in G 2. THEOREM C G n is dense in Aut1(C n) in the topology of uniform convergence on compact subsets. THEOREM D If F:C n →C n .Fis entire. J(F)=1 and m∈N, there is S m∈G n such that .