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

2012/01/09 by Laura DeMarco, DeMarco, Laura, Aaron Schiff +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1201.1891

openalex publication_date 2012/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an algorithm for computing the Euler characteristic of the curves S_p in the space of cubic polynomials, consisting of all polynomials with a periodic critical point of period p. The curves were introduced in [Milnor, Bonifant-Kiwi-Milnor], and the algorithm applies the main results of [DeMarco-Pilgrim]. The output is shown for periods p ≤ 26.

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