Baker domains and non-convergent deformations

  • Rodrigo Robles

    Universidad Nacional Autonoma de México, Ciudad de Mexico, Mexico
  • Guillermo Sienra

    Universidad Nacional Autonoma de México, Ciudad de Mexico, Mexico
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Abstract

For an entire transcendental function ff with a non-completely invariant Baker domain UU, we study the pinching process of paths in UU with certain restrictions, that we call Baker laminations. We show that if some curve in the Baker lamination of ff joins a point in the boundary of UU with infinity, then the deformation does not converge. Thus, in this particular case, the boundary of the space of deformations of ff is incomplete.

Cite this article

Rodrigo Robles, Guillermo Sienra, Baker domains and non-convergent deformations. J. Fractal Geom. 9 (2022), no. 1/2, pp. 1–23

DOI 10.4171/JFG/115