ACTA issues

Shabat polynomials and conformal mapping

Gerd Jensen, Christian Pommerenke

Acta Sci. Math. (Szeged) 85:1-2(2019), 147-170

Abstract. In this paper a concise but systematic account of the relations between Shabat polynomials and plane trees is given, including the famous equivalence theorem for plane trees attributed to Riemann--Belyi--Grothendieck--Shabat. Furthermore, some analytical features of Shabat polynomials and metric properties of Shabat trees are discussed.

DOI: 10.14232/actasm-017-821-6

AMS Subject Classification (1991): 05C05, 05C10, 30C10, 30C85, 30F99

Keyword(s): Shabat polynomials, plane trees, conformal mapping

Received November 11, 2017 and in final form February 7, 2018. (Registered under 71/2017.)