Abstract:
Connected Julia sets of a polynomial generally correspond to laminations, sets of chords of the unit disc that reflect the dynamics of the Julia set. If the circle is measured in revolutions and the polynomials studied are of degree $d$, then the dynamics on the lamination are given by the covering map $\sigma_d(t) := td \pmod 1$ where chords are mapped by their end points. Every lamination has at least one laminational invariant set, which is loosely an invariant complementary component of the lamination. That set has a significant impact on the shape of the Julia set. James Malaugh showed how to topologically transform a laminational invariant set in one degree into one in another degree, but he provided no way to execute these operations concretely. In this talk, we show how to calculate those operations.
Scheduled for: 2026-03-11 04:15 PM: Dynamics Session #2.2 in Heritage Hall Building 121
Status: Accepted
Collection: Dynamical Systems
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