### Abstract

Let be a dominant rational self-map of a smooth projective variety defined over. For each point whose forward -orbit is well defined, Silverman introduced the arithmetic degree, which measures the growth rate of the heights of the points. Kawaguchi and Silverman conjectured that is well defined and that, as varies, the set of values obtained by is finite. Based on constructions by Bedford and Kim and by McMullen, we give a counterexample to this conjecture when.

Original language | English (US) |
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Journal | Ergodic Theory and Dynamical Systems |

DOIs | |

State | Published - Jan 1 2019 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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**A rational map with infinitely many points of distinct arithmetic degrees.** / Lesieutre, John; Satriano, Matthew.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A rational map with infinitely many points of distinct arithmetic degrees

AU - Lesieutre, John

AU - Satriano, Matthew

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Let be a dominant rational self-map of a smooth projective variety defined over. For each point whose forward -orbit is well defined, Silverman introduced the arithmetic degree, which measures the growth rate of the heights of the points. Kawaguchi and Silverman conjectured that is well defined and that, as varies, the set of values obtained by is finite. Based on constructions by Bedford and Kim and by McMullen, we give a counterexample to this conjecture when.

AB - Let be a dominant rational self-map of a smooth projective variety defined over. For each point whose forward -orbit is well defined, Silverman introduced the arithmetic degree, which measures the growth rate of the heights of the points. Kawaguchi and Silverman conjectured that is well defined and that, as varies, the set of values obtained by is finite. Based on constructions by Bedford and Kim and by McMullen, we give a counterexample to this conjecture when.

UR - http://www.scopus.com/inward/record.url?scp=85065258676&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065258676&partnerID=8YFLogxK

U2 - 10.1017/etds.2019.30

DO - 10.1017/etds.2019.30

M3 - Article

AN - SCOPUS:85065258676

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

ER -