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Asymptotic Behavior of One-Parameter Semigroups and Rigidity of Holomorphic Generators

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Abstract.

We study the asymptotic behavior of one-parameter continuous semigroups of holomorphic mappings. We present angular characteristics of their trajectories at their Denjoy–Wolff points, as well as at their regular repelling points (whenever they exist). This enables us to establish new rigidity properties of holomorphic generators via the asymptotic behavior of the semigroups they generate.

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Authors and Affiliations

  1. Department of Mathematics, ORT Braude College, P.O. Box 78, IL-21982, Karmiel, Israel

    Mark Elin & David Shoikhet

  2. Department of Mathematics, The Technion – Israel Institute of Technology, IL-32000, Haifa, Israel

    Simeon Reich

  3. Department of Software Engineering, ORT Braude College, P.O. Box 78, IL-21982, Karmiel, Israel

    Fiana Yacobzon

Authors
  1. Mark Elin
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  2. Simeon Reich
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  3. David Shoikhet
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  4. Fiana Yacobzon
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Corresponding author

Correspondence to Simeon Reich.

Additional information

Communicated by Daniel Alpay.

Received: May 11, 2007. Accepted: July 22, 2007.

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Elin, M., Reich, S., Shoikhet, D. et al. Asymptotic Behavior of One-Parameter Semigroups and Rigidity of Holomorphic Generators. Complex anal.oper. theory 2, 55–86 (2008). https://doi.org/10.1007/s11785-007-0027-9

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  • DOI: https://doi.org/10.1007/s11785-007-0027-9

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