# 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

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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

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- [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

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