Genadi Levin
Published 2023-12-28Version 1
We notice that the main result of [G.M. Levin, Symmetries on the Julia set, Math. Notes 1990] holds for attractors of holomorphic iterated function systems (IFS) on the plane. Namely, either any non-trivial family of holomorphic local symmetries of the attractor is finite or the attractor contains an analytic arc. In fact, the same holds for any J-like compact subset of the plane.
Analytic families of holomorphic iterated function systems
Large scaled geometry of Julia sets of entire and meromorphic functions
A Core Decomposition of Compact Sets in the Plane
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