  A scattering zipper is a system obtained by concatenation of scattering
events with equal even number of incoming and out going channels. The
associated scattering zipper operator is the unitary equivalent of Jacobi
matrices with matrix entries and generalizes Blatter-Browne and
Chalker-Coddington models and CMV matrices. Weyl discs are analyzed and used to
prove a bijection between the set of semi-infinite scattering zipper operators
and matrix valued probability measures on the unit circle. Sturm-Liouville
oscillation theory is developed as a tool to calculate the spectra of finite
and periodic scattering zipper operators.
