Conjecture on the number of ergodic equilibrium states for singular value potentials
Let (A1,…,AN)∈GLd(R)(A_1,\ldots,A_N)\in GL_d(\mathbb{R})(A1,…,AN)∈GLd(R) and let s∈(0,d)∖Zs\in(0,d)\smallsetminus\mathbb{Z}s∈(0,d)∖Z. For a tuple of matrices, let φs\varphi^sφs denote Falconer's singular value function, and call…