Maps conjugating holomorphic maps in C^n

dc.creatorBuzzard, Gregery T.
dc.creatorMerenkov, Sergei
dc.date2003-01-13
dc.date2003-11-10
dc.date.accessioned2026-07-07T04:54:24Z
dc.date.available2026-07-07T04:54:24Z
dc.descriptionIf 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.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0301120
dc.identifierhttp://arxiv.org/abs/math/0301120
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66240
dc.subjectComplex Variables
dc.subjectDynamical Systems
dc.subject32H02; 32H50
dc.titleMaps conjugating holomorphic maps in C^n
dc.typetext

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