A rational map with infinitely many points of distinct arithmetic degrees

John Lesieutre, Matthew Satriano

Research output: Contribution to journalArticle


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)
JournalErgodic Theory and Dynamical Systems
Publication statusPublished - Jan 1 2019


All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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