A rational map with infinitely many points of distinct arithmetic degrees

John Lesieutre, Matthew Satriano

Research output: Contribution to journalArticle

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)
JournalErgodic Theory and Dynamical Systems
DOIs
StatePublished - Jan 1 2019

Fingerprint

Rational Maps
Well-defined
Orbits
Distinct
Projective Variety
Counterexample
Orbit
Vary

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.

In: Ergodic Theory and Dynamical Systems, 01.01.2019.

Research output: Contribution to journalArticle

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