Ergodicity, numerical range, and fixed points of holomorphic mappings |
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Authors: | Simeon Reich David Shoikhet Jaroslav Zemánek |
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Affiliation: | 19. Department of Mathematics, The Technion — Israel Institute of Technology, 32000, Haifa, Israel 29. Department of Mathematics, Ort Braude College, 21982, Karmiel, Israel 39. Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21, 00-956, Warszawa, Poland
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Abstract: | In this paper, we study the local structure of the fixed point set of a holomorphic mapping defined on a (not necessarily bounded or convex) domain in a complex Banach space, using ergodic theory of linear operators and the nonlinear numerical range introduced by L. A. Harris. We provide several constructions of holomorphic retractions and a generalization of Cartan’s Uniqueness Theorem. We also estimate the deviation of a holomorphic mapping from its linear approximation, the Fréchet derivative at a fixed point. |
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