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Dynamical generation of parameter laminations

Ch. 13. P. 205–229.
Blokh A., Oversteegen L., Timorin V.

Local similarity between the Mandelbrot set and quadratic Julia sets manifests itself in a variety of ways. We discuss a combinatorial one, in the language of geodesic laminations. More precisely, we compare quadratic invariant
laminations representing Julia sets with the so-called Quadratic Minor Lamination (QML) representing a locally connected model of the Mandelbrot set. Similarly to the construction of an invariant lamination by pullbacks of
certain leaves, we describe how QML can be generated by properly understood pullbacks of certain minors. In particular, we show that the minors of all non-renormalizable quadratic laminations can be obtained by taking limits
of “pullbacks” of minors from the main cardioid.

Language: English
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DOI
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Keywords: Julia setMandelbrot setinvariant laminationscomplex dynamics
Publication based on the results of:
Алгебраическая геометрия и ее приложения (2018)

In book

Contemporary Mathematics 744 Dynamics: Topology and Numbers (2020)
Contemporary Mathematics 744 Dynamics: Topology and Numbers (2020)
United States of America: American Mathematical Society, 2020.
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