Maps conjugating holomorphic maps in C^n
| dc.creator | Buzzard, Gregery T. | |
| dc.creator | Merenkov, Sergei | |
| dc.date | 2003-01-13 | |
| dc.date | 2003-11-10 | |
| dc.date.accessioned | 2026-07-07T04:54:24Z | |
| dc.date.available | 2026-07-07T04:54:24Z | |
| dc.description | If f is a bijection from C^n onto a complex manifold M, which conjugates every holomorphic map in C^n to an endomorphism in M, then we prove that f is necessarily biholomorphic or antibiholomorphic. This extends a result of A. Hinkkanen to higher dimensions. As a corollary, we prove that if there is an epimorphism from the semigroup of all holomorphic endomorphisms of C^n to the semigroup of holomorphic endomorphisms in M, or an epimorphism in the opposite direction for a doubly-transitive M, then it is given by conjugation by some biholomorphic or antibiholomorphic map. We show also that there are two unbounded domains in C^n with isomorphic endomorphism semigroups but which are neither biholomorphically nor antibiholomorphically equivalent. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0301120 | |
| dc.identifier | http://arxiv.org/abs/math/0301120 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66240 | |
| dc.subject | Complex Variables | |
| dc.subject | Dynamical Systems | |
| dc.subject | 32H02; 32H50 | |
| dc.title | Maps conjugating holomorphic maps in C^n | |
| dc.type | text |