## Abstract

Let A, B be matrices in SL2ℝ 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 2 B, AB 2}. In particular, it holds for every pair of 2 × 2 matrices with nonnegative integer entries and determinant 1.

Original language | English |
---|---|

Pages (from-to) | 5234-5260 |

Number of pages | 27 |

Journal | Nonlinearity |

Volume | 34 |

Issue number | 8 |

Early online date | 2 Jul 2021 |

DOIs | |

Publication status | Published - Aug 2021 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2021 IOP Publishing Ltd & London Mathematical Society.

## Keywords

- 15A60
- 37F32
- finiteness conjecture
- hyperbolic plane
- translation length Mathematics Subject Classification numbers: 05A05

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