English

Ergodicity and Algebraticity of the Fast and Slow Triangle Maps

Dynamical Systems 2024-09-24 v2 Number Theory

Abstract

Our goal is to show that both the fast and slow versions of the triangle map (a type of multi-dimensional continued fraction algorithm) in dimension nn are ergodic, resolving a conjecture of Messaoudi, Noguiera and Schweiger. This particular type of higher dimensional multi-dimensional continued fraction algorithm has recently been linked to the study of partition numbers, with the result that the underlying dynamics has combinatorial implications.

Keywords

Cite

@article{arxiv.2409.05822,
  title  = {Ergodicity and Algebraticity of the Fast and Slow Triangle Maps},
  author = {Thomas Garrity and Jacob Lehmann Duke},
  journal= {arXiv preprint arXiv:2409.05822},
  year   = {2024}
}

Comments

An all important word "not" was added to a sentence on the second page of the first version