Evolution Semigroups in Dynamical Systems and Differential Equations
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 infinite-dimensional nonautonomous problems, which is based on the consistent use of evolution semigroups. This unifying idea connects various questions in stability of semigroups, infinite-dimensional hyperbolic linear skew-product flows, translation Banach algebras, transfer operators, stability radii in control theory, Lyapunov exponents, magneto-dynamics and hydro-dynamics.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 skew-product 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 non-traditional applications are provided.
- Hardback | 361 pages
- 177.8 x 254 x 25.4mm | 861.83g
- 15 Aug 1999
- American Mathematical Society
- Providence, United States
- bibliograph, notes, index
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 skew-product flows and Mather evolution semigroups Characterizations of dichotomy for linear skew-product flows Evolution operators and exact Lyapunov exponents Bibliography List of notations Index.