Title

Non-Autonomous julia sets with measurable invariant sequences of line fields

Document Type

Article

Date of Original Version

1-1-2013

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 coeficients. 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 with at most countably many points removed.

Publication Title

Discrete and Continuous Dynamical Systems- Series A

Volume

33

Issue

2

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