Geometry of the locus of polynomials of degree 4 with iterative roots

• Autorzy: Beata Strycharz-Szemberg , Tomasz Szemberg
• Języki publikacji: EN

Abstrakty

EN

We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.

Słowa kluczowe

EN

Iterative roots; Complex polynomials

Kategorie tematyczne

• 30D05: Functional equations in the complex domain, iteration and composition of analytic functions
• 39B12: Iteration theory, iterative and composite equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 2
• Strony: 338-345

Daty

wydano

2011-04-01

online

2011-02-18

Twórcy

autor

Beata Strycharz-Szemberg

• Politechnika Krakowska

autor

Tomasz Szemberg

Bibliografia

• [1] Babbage C., Examples of the Solution of Functional Equations, Cambridge, 1820
• [2] Bronshteĭn E.M., On an iterative square root of a quadratic trinomial, In: Geometric Problems in the Theory of Functions and Sets, Kalinin. Gos. Univ., Kalinin, 1989, 24–27 (in Russian)
• [3] Chen X., Shi Y, Zhang W., Planar quadratic degree-preserving maps and their iteration, Results Math., 2009, 55(1–2), 39–63 http://dx.doi.org/10.1007/s00025-009-0389-6
• [4] Choczewski B., Kuczma M., On iterative roots of polynomials, In: European Conference on Iteration Theory, Lisbon, 15–21 September 1991, World Scientific, Singapore-New Jersey-London-Hong Kong, 1992, 59–67
• [5] Decker W., Greuel G.-M., Pfister G., Schönemann, H., Singular 3-1-1 - A Computer Algebra System for Polynomial Computations, available at http://www.singular.uni-kl.de
• [6] Hulek K., Elementary Algebraic Geometry, Stud. Math. Libr., 20, AMS, Providence, 2003
• [7] Rice R.E., Schweizer B., Sklar A., When is f(f(z)) = az 2 + bz + c?, Amer. Math. Monthly, 1980, 87(4), 252–263 http://dx.doi.org/10.2307/2321556

Identyfikatory

DOI

10.2478/s11533-010-0093-5