Nonuniform dichotomy spectrum and reducibility for nonautonomous   difference equations
  For nonautonomous linear difference equations, we introduce the notion of the so-called nonuniform dichotomy spectrum and prove a spectral theorem. Moreover, we introduce the notion of weak kinematical similarity and prove a reducibility result by the spectral theorem. 
Jifeng Chu, Hailong Zhu, Stefan Siegmund, Yonghui Xia
math.DS