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1 results

  • 23 - Dynamical Rigidity of Compactly Nonrecurrent Regular Elliptic Functions

  • from Part VI - Compactly Nonrecurrent Elliptic Functions: Fractal Geometry, Stochastic Properties, and Rigidity
  • Janina Kotus, Warsaw University of Technology, Mariusz Urbański, University of North Texas
  • Book:
    Meromorphic Dynamics
    Published online:
    20 April 2023
    Print publication:
    04 May 2023, pp 458-488

  • Summary

    In this chapter, we deal with the dynamical rigidity of compactly nonrecurrent regular elliptic functions. The issue at stake is whether a weak conjugacy such as a Lipschitz one on Julia sets can be promoted to a much better one such as affine on the whole complex plane $\C$. This topic has a long history and goes back at least to the seminal paper by Sullivan, treating among others the dynamical rigidity of conformal expanding repellers. Our approach in this chapter stems from this article by Sullivan.