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2 results on '"Caractérisation des automorphismes analytiques par la suite des itérés"'

1. Sur les automorphismes analytiques des variétés hyperboliques

Author

Loeb, Jean-Jacques and Vigué, Jean-Pierre

Subjects
*COMPARISON (Psychology), *ATTENTION, *CONSCIOUSNESS, *THEORY of knowledge
Abstract

Abstract: Results of H. Cartan about holomorphic automorphisms on bounded domains are generalized to the case of hyperbolic manifolds in the sense of Kobayashi. In this setting, we give an identity theorem together with its topological version. We show also that a sequence of automorphisms which converges uniformly on some nonempty open set, has a limit on the whole space which is an automorphism. At the end of the paper, conditions are given for the sequence of iterates of a self holomorphic map in order to be an automorphism. [Copyright &y& Elsevier]

Published
2007
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2. Sur les automorphismes analytiques des variétés hyperboliques

Author

Jean-Pierre Vigué and Jean-Jacques Loeb

Subjects
Sequence, Pure mathematics, Mathematics(all), Mathematics::Complex Variables, General Mathematics, Mathematical analysis, Holomorphic function, Open set, Limit of analytic automorphisms, Caractérisation des automorphismes analytiques par la suite des itérés, Automorphism, Identity theorem, Limites d'automorphismes analytiques, Variétés hyperboliques, Mathematics::Group Theory, Iterated function, Bounded function, Hyperbolic manifolds, Limit (mathematics), Characterization of analytic automorphisms by the sequence of iterates, Mathematics
Abstract

Results of H. Cartan about holomorphic automorphisms on bounded domains are generalized to the case of hyperbolic manifolds in the sense of Kobayashi. In this setting, we give an identity theorem together with its topological version. We show also that a sequence of automorphisms which converges uniformly on some nonempty open set, has a limit on the whole space which is an automorphism. At the end of the paper, conditions are given for the sequence of iterates of a self holomorphic map in order to be an automorphism.

Published
2007
Full Text
View/download PDF

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