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Erschienen in:
2019 | OriginalPaper | Buchkapitel
Semigroups of Holomorphic Mappings
verfasst von : Mark Elin, Simeon Reich, David Shoikhet
Erschienen in: Numerical Range of Holomorphic Mappings and Applications
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In this chapter we consider certain autonomous dynamical systems acting on the open unit ball of a complex Banach space. Our interest in such systems is based on the fact that if a dynamical system is differentiable with respect to time, then its derivative is a holomorphically dissipative mapping. Furthermore, different estimates on the numerical range lead to rather detailed information on the asymptotic behavior of the system. We pay special attention to stationary points of dynamical systems and to so-called flow invariance conditions.