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Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations

  • Book
  • © 1999

Overview

Authors:
  1. Constantin Vârsan

    1. Institute of Mathematics, Romanian Academy, Bucharest, Romania

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Part of the book series: Mathematics and Its Applications (MAIA, volume 466)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Constantin Vârsan
    Pages 1-4

  3. Gradient Systems in a Lie Algebra

    • Constantin Vârsan
    Pages 5-23

  4. Representation of a Gradient System

    • Constantin Vârsan
    Pages 25-48

  5. Finitely Generated over Orbits Lie Algebras and Algebraic Representation of the Gradient System

    • Constantin Vârsan
    Pages 49-75

  6. Applications

    • Constantin Vârsan
    Pages 77-115

  7. Stabilization and Related Problems

    • Constantin Vârsan
    Pages 117-195

  8. Back Matter

    Pages 197-243
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Keywords

About this book

The main part of the book is based on a one semester graduate course for students in mathematics. I have attempted to develop the theory of hyperbolic systems of differen­ tial equations in a systematic way, making as much use as possible ofgradient systems and their algebraic representation. However, despite the strong sim­ ilarities between the development of ideas here and that found in a Lie alge­ bras course this is not a book on Lie algebras. The order of presentation has been determined mainly by taking into account that algebraic representation and homomorphism correspondence with a full rank Lie algebra are the basic tools which require a detailed presentation. I am aware that the inclusion of the material on algebraic and homomorphism correspondence with a full rank Lie algebra is not standard in courses on the application of Lie algebras to hyperbolic equations. I think it should be. Moreover, the Lie algebraic structure plays an important role in integral representation for solutions of nonlinear control systems and stochastic differential equations yelding results that look quite different in their original setting. Finite-dimensional nonlin­ ear filters for stochastic differential equations and, say, decomposability of a nonlinear control system receive a common understanding in this framework.

Authors and Affiliations

  • Institute of Mathematics, Romanian Academy, Bucharest, Romania

    Constantin Vârsan

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