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) |
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Pages (from-to) | 99-111 |
Number of pages | 13 |
Journal | Experimental Mathematics |
Volume | 22 |
Issue number | 1 |
DOIs | |
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