Stability of Nonautonomous Differential Equations

Luis Barreira is a Full Professor of Mathematics at Instituto Superior Tecnico, Lisbon and a member of the Center for Mathematical Analysis, Geometry, and Dynamical Systems. He obtained his PhD from the Pennsylvania State University in 1996. In 2007 he has been awarded the Gulbenkian Science Prize. Claudia Valls is an Invited Assistant Professor at Instituto Superior Tecnico, Lisbon and a Postdoctoral Fellow at the Center for Mathematical Analysis, Geometry, and Dynamical Systems, of which she is also a member. She obtained her PhD from the Universitat de Barcelona in 1999.

• Exponential 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.

From 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)