Geometry of the locus of polynomials of degree 4 with iterative roots
Beata Strycharz-Szemberg ; Tomasz Szemberg
Open Mathematics, Tome 9 (2011), p. 338-345 / Harvested from The Polish Digital Mathematics Library

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

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:269688
@article{bwmeta1.element.doi-10_2478_s11533-010-0093-5,
     author = {Beata Strycharz-Szemberg and Tomasz Szemberg},
     title = {Geometry of the locus of polynomials of degree 4 with iterative roots},
     journal = {Open Mathematics},
     volume = {9},
     year = {2011},
     pages = {338-345},
     zbl = {1234.30026},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0093-5}
}
Beata Strycharz-Szemberg; Tomasz Szemberg. Geometry of the locus of polynomials of degree 4 with iterative roots. Open Mathematics, Tome 9 (2011) pp. 338-345. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0093-5/

[1] Babbage C., Examples of the Solution of Functional Equations, Cambridge, 1820 | Zbl 0018.16903

[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 | Zbl 1190.39009

[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 | Zbl 0902.14040

[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 | Zbl 0441.30033