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Working paper

Plane trees, Shabat-Zapponi polynomials and Julia sets

arxiv.org. math. Cornell University, 2016. No. 1608.08866.
A tree, embedded into plane, is a dessin d'enfant and its Belyi function is a polynomial -- Shabat polynomial. Zapponi form of this polynomial is unique, so we can correspond to an embedded tree the Julia set of its Shabat-Zapponi polynomial. In this purely experimental work we study relations between the form of a tree and properties (form, connectedness, Hausdorff dimension) of its Julia set.