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Complex dynamical systems and the geometry of domains in Banach spaces

Tom 427 / 2004

Mark Elin, Simeon Reich, David Shoikhet Dissertationes Mathematicae 427 (2004), 1-62 MSC: 30C45, 32F45, 34G20, 46G20, 46T25, 47H20. DOI: 10.4064/dm427-0-1

Streszczenie

We consider semigroups of holomorphic self-mappings on domains in Hilbert and Banach spaces, and then develop a new dynamical approach to the study of geometric properties of biholomorphic mappings. We establish, for example, several flow invariance conditions and find parametric representations of semicomplete vector fields. In order to examine the asymptotic behavior of these semigroups, we use diverse tools such as hyperbolic metric theory and estimates of solutions of generalized differential equations. In addition, we introduce a new method involving admissible upper and lower bounds. Finally, we apply our dynamical approach to obtain several growth and covering theorems for star-like mappings on the open unit balls of Banach and Hilbert spaces.

Autorzy

  • Mark ElinDepartment of Mathematics
    ORT Braude College
    21982 Karmiel, Israel
    e-mail
  • Simeon ReichDepartment of Mathematics
    The Technion – Israel Institute of Technology
    32000 Haifa, Israel
    e-mail
  • David ShoikhetDepartment of Mathematics
    ORT Braude College
    21982 Karmiel, Israel
    e-mail

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