Mathematical Surveys and Monographs 1999; 361 pp; hardcover Volume: 70 ISBN10: 0821811851 ISBN13: 9780821811856 List Price: US$91 Member Price: US$72.80 Order Code: SURV/70
 The main theme of the book is the spectral theory for evolution operators and evolution semigroups, a subject tracing its origins to the classical results of J. Mather on hyperbolic dynamical systems and J. Howland on nonautonomous Cauchy problems. The authors use a wide range of methods and offer a unique presentation. The authors give a unifying approach for a study of infinitedimensional nonautonomous problems, which is based on the consistent use of evolution semigroups. This unifying idea connects various questions in stability of semigroups, infinitedimensional hyperbolic linear skewproduct flows, translation Banach algebras, transfer operators, stability radii in control theory, Lyapunov exponents, magnetodynamics and hydrodynamics. Thus the book is much broader in scope than existing books on asymptotic behavior of semigroups. Included is a solid collection of examples from different areas of analysis, PDEs, and dynamical systems. This is the first monograph where the spectral theory of infinite dimensional linear skewproduct flows is described together with its connection to the multiplicative ergodic theorem; the same technique is used to study evolution semigroups, kinematic dynamos, and Ruelle operators; the theory of stability radii, an important concept in control theory, is also presented. Examples are included and nontraditional applications are provided. Readership Graduate students and research mathematicians interested in the theory of strongly continuous semigroups of linear operators and evolution equations, Banach and \(C^*\)algebras, infinitedimensional and hyperbolic dynamical systems, control theory and ergodic theory; engineers, and physicists interested in Lyapunov exponents, transfer operators, etc. Reviews "It was a pleasure to read this monograph, which is written in an agreeable and consistent style ... This excellent exposition should serve as a reference book for further research in these fields employing the powerful methods presented by Chicone and Latushkin."  Mathematical Reviews Table of Contents  Introduction
 Semigroups on Banach spaces and evolution semigroups
 Evolution families and Howland semigroups
 Characterizations of dichotomy for evolution families
 Two applications of evolution semigroups
 Linear skewproduct flows and Mather evolution semigroups
 Characterizations of dichotomy for linear skewproduct flows
 Evolution operators and exact Lyapunov exponents
 Bibliography
 List of notations
 Index
