The geometry of the critically periodic curves in the space of cubic polynomials

Laura De Marco; Aaron Schiff

doi:10.1080/10586458.2013.743857

The geometry of the critically periodic curves in the space of cubic polynomials

Laura De Marco^*, Aaron Schiff

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We provide an algorithm for computing the Euler characteristic of the curves in consisting of all polynomials with a periodic critical point of period p in the space of critically marked complex cubic polynomials. The curves were introduced in [Milnor 09, Bonifant et al. 10], and the algorithm applies the main results of [DeMarco and Pilgrim 11b]. The output is shown for periods p≤26.

Original language	English (US)
Pages (from-to)	99-111
Number of pages	13
Journal	Experimental Mathematics
Volume	22
Issue number	1
DOIs	https://doi.org/10.1080/10586458.2013.743857
State	Published - Jan 1 2013

Keywords

Euler characteristic
cubic polynomial
periodic critical point
pictograph
tau function

ASJC Scopus subject areas

Mathematics(all)

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10.1080/10586458.2013.743857

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abstract = "We provide an algorithm for computing the Euler characteristic of the curves in consisting of all polynomials with a periodic critical point of period p in the space of critically marked complex cubic polynomials. The curves were introduced in [Milnor 09, Bonifant et al. 10], and the algorithm applies the main results of [DeMarco and Pilgrim 11b]. The output is shown for periods p≤26.",

keywords = "Euler characteristic, cubic polynomial, periodic critical point, pictograph, tau function",

author = "{De Marco}, Laura and Aaron Schiff",

note = "Funding Information: We would like to thank Jan Kiwi, Jack Milnor, and Kevin Pilgrim for helpful conversations and attention to the output. We would also like to thank the referee for a careful reading and useful suggestions, especially for the arguments in Section 2. This research was supported by the National Science Foundation.",

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AU - De Marco, Laura

AU - Schiff, Aaron

N1 - Funding Information: We would like to thank Jan Kiwi, Jack Milnor, and Kevin Pilgrim for helpful conversations and attention to the output. We would also like to thank the referee for a careful reading and useful suggestions, especially for the arguments in Section 2. This research was supported by the National Science Foundation.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We provide an algorithm for computing the Euler characteristic of the curves in consisting of all polynomials with a periodic critical point of period p in the space of critically marked complex cubic polynomials. The curves were introduced in [Milnor 09, Bonifant et al. 10], and the algorithm applies the main results of [DeMarco and Pilgrim 11b]. The output is shown for periods p≤26.

AB - We provide an algorithm for computing the Euler characteristic of the curves in consisting of all polynomials with a periodic critical point of period p in the space of critically marked complex cubic polynomials. The curves were introduced in [Milnor 09, Bonifant et al. 10], and the algorithm applies the main results of [DeMarco and Pilgrim 11b]. The output is shown for periods p≤26.

KW - Euler characteristic

KW - cubic polynomial

KW - periodic critical point

KW - pictograph

KW - tau function

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JO - Experimental Mathematics

JF - Experimental Mathematics

SN - 1058-6458

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The geometry of the critically periodic curves in the space of cubic polynomials

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Keywords

ASJC Scopus subject areas

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