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Semidynamical Systems in Infinite Dimensional Spaces

  • Book
  • © 1981

Overview

Authors:
  1. Stephen H. Saperstone

    1. Department of Mathematics, George Mason University, Fairfax, USA

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Part of the book series: Applied Mathematical Sciences (AMS, volume 37)

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Table of contents (8 chapters)

  1. Front Matter

    Pages N1-xiii
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  2. Basic Definitions and Properties

    • Stephen H. Saperstone
    Pages 1-34

  3. Invariance, Limit Sets, and Stability

    • Stephen H. Saperstone
    Pages 35-97

  4. Motions in Metric Space

    • Stephen H. Saperstone
    Pages 98-136

  5. Nonautonomous Ordinary Differential Equations

    • Stephen H. Saperstone
    Pages 137-208

  6. Semidynamical Systems in Banach Space

    • Stephen H. Saperstone
    Pages 209-282

  7. Functional Differential Equations

    • Stephen H. Saperstone
    Pages 283-368

  8. Stochastic Dynamical Systems

    • Stephen H. Saperstone
    Pages 369-392

  9. Weak Semidynamical Systems and Processes

    • Stephen H. Saperstone
    Pages 393-423

  10. Back Matter

    Pages 424-475
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Keywords

About this book

Where do solutions go, and how do they behave en route? These are two of the major questions addressed by the qualita­ tive theory of differential equations. The purpose of this book is to answer these questions for certain classes of equa­ tions by recourse to the framework of semidynamical systems (or topological dynamics as it is sometimes called). This approach makes it possible to treat a seemingly broad range of equations from nonautonomous ordinary differential equa­ tions and partial differential equations to stochastic differ­ ential equations. The methods are not limited to the examples presented here, though. The basic idea is this: Embed some representation of the solutions of the equation (and perhaps the equation itself) in an appropriate function space. This space serves as the phase space for the semidynamical system. The phase map must be chosen so as to generate solutions to the equation from an initial value. In most instances it is necessary to provide a "weak" topology on the phase space. Typically the space is infinite dimensional. These considerations motivate the requirement to study semidynamical systems in non locally compact spaces. Our objective here is to present only those results needed for the kinds of applications one is likely to encounter in differen­ tial equations. Additional properties and extensions of ab­ stract semidynamical systems are left as exercises. The power of the semidynamical framework makes it possible to character- Preface ize the asymptotic behavior of the solutions of such a wide class of equations.

Authors and Affiliations

  • Department of Mathematics, George Mason University, Fairfax, USA

    Stephen H. Saperstone

Bibliographic Information

  • Book Title: Semidynamical Systems in Infinite Dimensional Spaces

  • Authors: Stephen H. Saperstone

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4612-5977-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1981

  • Softcover ISBN: 978-0-387-90643-0Published: 16 November 1981

  • eBook ISBN: 978-1-4612-5977-0Published: 06 December 2012

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: 492

  • Topics: Theoretical, Mathematical and Computational Physics

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