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

5 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

Funding

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.

Keywords

Euler characteristic
cubic polynomial
periodic critical point
pictograph
tau function

ASJC Scopus subject areas

General Mathematics

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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.",

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AU - De Marco, Laura

AU - Schiff, Aaron

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

Abstract

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Keywords

ASJC Scopus subject areas

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