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Semigroups of Holomorphic Mappings

In: Numerical Range of Holomorphic Mappings and Applications

Author

Listed:
  • 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
    Holon Institute of Technology, Department of Mathematics)

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.

Suggested Citation

  • Mark Elin & Simeon Reich & David Shoikhet, 2019. "Semigroups of Holomorphic Mappings," Springer Books, in: Numerical Range of Holomorphic Mappings and Applications, chapter 0, pages 97-128, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-05020-7_4
    DOI: 10.1007/978-3-030-05020-7_4
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