naa a22 4500 51078156X CHVBK 20180411083249.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1007/s11854-013-0009-y doi (NATIONALLICENCE)springer-10.1007/s11854-013-0009-y Ergodicity, numerical range, and fixed points of holomorphic mappings [Elektronische Daten] [Simeon Reich, David Shoikhet, Jaroslav Zemánek] 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. Hebrew University Magnes Press, 2013 Reich Simeon Department of Mathematics, The Technion — Israel Institute of Technology, 32000, Haifa, Israel aut Shoikhet David Department of Mathematics, Ort Braude College, 21982, Karmiel, Israel aut Zemánek Jaroslav Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21, 00-956, Warszawa, Poland aut Journal d'Analyse Mathématique The Hebrew University Magnes Press 119/1(2013-04-01), 275-303 0021-7670 119:1<275 2013 119 11854 https://doi.org/10.1007/s11854-013-0009-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0009-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Reich Simeon Department of Mathematics, The Technion — Israel Institute of Technology, 32000, Haifa, Israel aut NATIONALLICENCE 700 1- Shoikhet David Department of Mathematics, Ort Braude College, 21982, Karmiel, Israel aut NATIONALLICENCE 700 1- Zemánek Jaroslav Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21, 00-956, Warszawa, Poland aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique The Hebrew University Magnes Press 119/1(2013-04-01), 275-303 0021-7670 119:1<275 2013 119 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer