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Published in:
2019 | OriginalPaper | Chapter
Ergodic Theory of Holomorphic Mappings
Authors : Mark Elin, Simeon Reich, David Shoikhet
Published in: Numerical Range of Holomorphic Mappings and Applications
Publisher: Springer International Publishing
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Ergodic approximations naturally associated with a given holomorphic mapping essentially determine the asymptotic behavior of the nonlinear mapping in a way similar to how the “big bang” seems to determine future developments. Most important among such approximations are those associated to fixed points of the given holomorphic mapping, stationary points of semigroups of holomorphic mappings, and null points of semigroup generators.