Joint spectral radius, Sturmian measures, and the finiteness conjecture

Oliver Jenkinson, Mark Pollicott

The joint spectral radius of a pair of 2x2 real matrices $(A_0,A_1)\in M_2(\mathbb{R}{)}^2$ is defined to be $r(A_0,A_1)= \limsup_{n\to\infty} \max \{\|A_{i_1}...A_{i_n}\|^{1/n}: i_j…