A rational map with infinitely many points of distinct arithmetic degrees

John Lesieutre, Matthew Satriano

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)3051-3055
Number of pages5
JournalErgodic Theory and Dynamical Systems
Volume40
Issue number11
DOIs
StatePublished - Nov 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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