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Evolution Semigroups in Dynamical Systems and Differential Equations
 
Carmen Chicone University of Missouri, Columbia, Columbia, MO
Yuri Latushkin University of Missouri, Columbia, Columbia, MO
Evolution Semigroups in Dynamical Systems and Differential Equations
Hardcover ISBN:  978-0-8218-1185-6
Product Code:  SURV/70
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1297-5
Product Code:  SURV/70.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-1185-6
eBook: ISBN:  978-1-4704-1297-5
Product Code:  SURV/70.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Evolution Semigroups in Dynamical Systems and Differential Equations
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Evolution Semigroups in Dynamical Systems and Differential Equations
Carmen Chicone University of Missouri, Columbia, Columbia, MO
Yuri Latushkin University of Missouri, Columbia, Columbia, MO
Hardcover ISBN:  978-0-8218-1185-6
Product Code:  SURV/70
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1297-5
Product Code:  SURV/70.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-1185-6
eBook ISBN:  978-1-4704-1297-5
Product Code:  SURV/70.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 701999; 361 pp
    MSC: Primary 47; 34; Secondary 58;

    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.

    Readership

    Graduate students and research mathematicians interested in the theory of strongly continuous semigroups of linear operators and evolution equations, Banach and \(C^*\)-algebras, infinite-dimensional and hyperbolic dynamical systems, control theory and ergodic theory; engineers, and physicists interested in Lyapunov exponents, transfer operators, etc.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Semigroups on Banach spaces and evolution semigroups
    • 3. Evolution families and Howland semigroups
    • 4. Characterizations of dichotomy for evolution families
    • 5. Two applications of evolution semigroups
    • 6. Linear skew-product flows and Mather evolution semigroups
    • 7. Characterizations of dichotomy for linear skew-product flows
    • 8. Evolution operators and exact Lyapunov exponents
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 701999; 361 pp
MSC: Primary 47; 34; Secondary 58;

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.

Readership

Graduate students and research mathematicians interested in the theory of strongly continuous semigroups of linear operators and evolution equations, Banach and \(C^*\)-algebras, infinite-dimensional and hyperbolic dynamical systems, control theory and ergodic theory; engineers, and physicists interested in Lyapunov exponents, transfer operators, etc.

  • Chapters
  • 1. Introduction
  • 2. Semigroups on Banach spaces and evolution semigroups
  • 3. Evolution families and Howland semigroups
  • 4. Characterizations of dichotomy for evolution families
  • 5. Two applications of evolution semigroups
  • 6. Linear skew-product flows and Mather evolution semigroups
  • 7. Characterizations of dichotomy for linear skew-product flows
  • 8. Evolution operators and exact Lyapunov exponents
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.