Wreath products and proportions of periodic points

By Jamie Juul, Pär Kurlberg, Kalyani Madhu, T. Tucker. 2014

52 citations recorded by the source corpus.

Let $\varphi: {\mathbb P}^1 \longrightarrow {\mathbb P}^1$ be a rational map of degree greater than one defined over a number field $k$. For each prime ${\mathfrak p}$ of good reduction for $\varphi$, we let $\varphi_{\mathfrak p}$ denote the reduction of $\varphi$ modulo ${\mathfrak p}$. A random map heuristic suggests that for large ${\mathfrak p}$, the proportion of periodic points of $\varphi_{\mathfrak p}$ in ${\mathbb P}^1({\mathfrak o}_k/{\mathfrak p})$ should be small. We show that this is indeed the case for many rational functions $\varphi$.

Subfields: Algebra and Number Theory, Artificial Intelligence, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d45e0a3669997a3e912fa4ddc0c00125c5c98db8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

  1. Laura Demarco
  2. T. Tucker
  3. Joseph H. Silverman
  4. Rafe Jones
  5. Patrick Ingram
  6. Robert L. Benedetto
  7. Michelle Manes
  8. Franccois Berteloot

In Artificial Intelligence

  1. Robert L. Benedetto
  2. Rafe Jones
  3. Laura Demarco

In Geometry and Topology

  1. T. Tucker
  2. Robert L. Benedetto
  3. Laura Demarco
  4. Joseph H. Silverman
  5. Michelle Manes
  6. Rafe Jones
  7. Patrick Ingram
  8. Franccois Berteloot

Citations in the corpus