Geometry of the locus of polynomials of degree 4 with iterative roots
Beata Strycharz-Szemberg; Tomasz Szemberg
Open Mathematics (2011)
- Volume: 9, Issue: 2, page 338-345
- ISSN: 2391-5455
Access Full Article
top
Abstract
topHow to cite
topBeata Strycharz-Szemberg, and Tomasz Szemberg. "Geometry of the locus of polynomials of degree 4 with iterative roots." Open Mathematics 9.2 (2011): 338-345. <http://eudml.org/doc/269688>.
@article{BeataStrycharz2011,
abstract = {We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.},
author = {Beata Strycharz-Szemberg, Tomasz Szemberg},
journal = {Open Mathematics},
keywords = {Iterative roots; Complex polynomials; iterative roots; complex polynomials},
language = {eng},
number = {2},
pages = {338-345},
title = {Geometry of the locus of polynomials of degree 4 with iterative roots},
url = {http://eudml.org/doc/269688},
volume = {9},
year = {2011},
}
TY - JOUR
AU - Beata Strycharz-Szemberg
AU - Tomasz Szemberg
TI - Geometry of the locus of polynomials of degree 4 with iterative roots
JO - Open Mathematics
PY - 2011
VL - 9
IS - 2
SP - 338
EP - 345
AB - We study polynomial iterative roots of polynomials and describe the locus of complex polynomials of degree 4 admitting a polynomial iterative square root.
LA - eng
KW - Iterative roots; Complex polynomials; iterative roots; complex polynomials
UR - http://eudml.org/doc/269688
ER -
References
top- [1] Babbage C., Examples of the Solution of Functional Equations, Cambridge, 1820 Zbl0018.16903
- [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 Zbl1190.39009
- [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 Zbl0902.14040
- [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 Zbl0441.30033
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.