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Non-Autonomous Julia Sets with Invariant Sequences of Measurable Line Fields

Authors
  • Comerford, Mark
Type
Preprint
Publication Date
May 22, 2011
Submission Date
May 16, 2011
Identifiers
arXiv ID: 1105.3225
Source
arXiv
License
Yellow
External links

Abstract

The no invariant line fields conjecture is one of the main outstanding problems in traditional complex dynamics. In this paper we consider non-autonomous iteration where one works with compositions of sequences of polynomials with suitable bounds on the degrees and coefficients. We show that the natural generalization of the no invariant line fields conjecture to this setting is not true. In particular, we construct a sequence of quadratic polynomials whose iterated Julia sets all have positive area and which has an invariant sequence of measurable line fields whose supports are these iterated Julia sets.

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