Volume-preserving automorphisms of C⊃n⊃
- 1 April 1990
- journal article
- research article
- Published by Taylor & Francis in Complex Variables and Elliptic Equations
- Vol. 14 (1-4) , 223-235
- https://doi.org/10.1080/17476939008814422
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 .Keywords
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