Nonuniform $(h,k,\mu ,\nu )$-Dichotomy with Applications to Nonautonomous Dynamical Systems

Abstract

The paper develops and studies a very general notion of dichotomy, referred to as "nonuniform $(h,k,\mu ,\nu )$-dichotomy". The new notion contains as special cases most versions of dichotomy existing in the literature. The paper then provides corresponding new versions of robustness, Hartman-Grobman theorem, and stable manifold theorem for nonautonomous dynamical systems in Banach spaces in term of the nonuniform $(h,k,\mu ,\nu )$-dichotomy.