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

Laura De Marco*, Aaron Schiff

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)99-111
Number of pages13
JournalExperimental Mathematics
Volume22
Issue number1
DOIs
StatePublished - 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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