The finiteness conjecture holds in SL(2,Z>=0)^2

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).

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 The ArXiv version is outdated, but we cannot replace it due to copyright reasons.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

References in corpus (3)

• The joint spectrum
• Hourglass alternative and the finiteness conjecture for the spectral characteristics of sets of non-negative matrices
• Minimax joint spectral radius and stabilizability of discrete-time linear switching control systems

Cited by in corpus (1)

• Partial classification of spectrum maximizing products for pairs of $2\times 2$ matrices