The finiteness conjecture holds in SL(2,Z>=0)^2
Dynamical Systems
2021-08-11 v2 Numerical Analysis
Group Theory
Numerical Analysis
Abstract
Let A,B be matrices in SL(2,R) having trace greater than or equal to 2. Assume the pair A,B is coherently oriented, that is, can be conjugated to a pair having nonnegative entries. Assume also that either A,B^(-1) is coherently oriented as well, or A,B have integer entries. Then the Lagarias-Wang finiteness conjecture holds for the set {A,B}, with optimal product in {A,B,AB,A^2B,AB^2}. In particular, it holds for every matrix pair in SL(2,Z>=0).
Cite
@article{arxiv.2006.16899,
title = {The finiteness conjecture holds in SL(2,Z>=0)^2},
author = {Giovanni Panti and Davide Sclosa},
journal= {arXiv preprint arXiv:2006.16899},
year = {2021}
}
Comments
To appear in Nonlinearity; we sincerely thank the referee for the precious remarks. The ArXiv version is outdated, but we cannot replace it due to copyright reasons. The final author-created, un-copyedited version of this paper is available from the first author's home page