Exponential dichotomy for dynamically defined matrix-valued Jacobi operators

In this paper, we present in this work a proof of the exponential dichotomy for a family of dynamically defined matrix-valued Jacobi operators in [Formula: see text], [Formula: see text], where [Formula: see text] is a compact metric space. Namely, we show that for each [Formula: see text], the resolvent set of [Formula: see text] corresponds to the subset of [Formula: see text] for which [Formula: see text], the [Formula: see text]-cocycle induced by the eigenvalue equation [Formula: see text] at [Formula: see text], is uniformly hyperbolic if [Formula: see text] is minimal.