Description
Book SynopsisThis volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.
Trade ReviewFrom the reviews: “In this book, the authors give a unified presentation of a substantial body of work which they have carried out and which revolves around the concept of nonuniform exponential dichotomy. … This is a well-written book which contains many interesting results. The reader will find significant generalizations of the standard invariant manifold theories, of the Hartman-Grobman theorem … . Anyone interested in these topics will profit from reading this book.” (Russell A. Johnson, Mathematical Reviews, Issue 2010 b)
Table of ContentsExponential dichotomies.- Exponential dichotomies and basic properties.- Robustness of nonuniform exponential dichotomies.- Stable manifolds and topological conjugacies.- Lipschitz stable manifolds.- Smooth stable manifolds in Rn.- Smooth stable manifolds in Banach spaces.- A nonautonomous Grobman–Hartman theorem.- Center manifolds, symmetry and reversibility.- Center manifolds in Banach spaces.- Reversibility and equivariance in center manifolds.- Lyapunov regularity and stability theory.- Lyapunov regularity and exponential dichotomies.- Lyapunov regularity in Hilbert spaces.- Stability of nonautonomous equations in Hilbert spaces.
