Semigroups of Holomorphic Mappings

Mark Elin, Simeon Reich and David Shoikhet
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Mark Elin: ORT Braude College, Department of Mathematics
Simeon Reich: The Technion - Israel Institute of Technology, Department of Mathematics
David Shoikhet: ORT Braude College, Department of Mathematics

Chapter Chapter 4 in Numerical Range of Holomorphic Mappings and Applications, 2019, pp 97-128 from Springer

Abstract: Abstract 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.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-05020-7_4

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DOI: 10.1007/978-3-030-05020-7_4

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