Ebook: Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations
Author: Constantin Vârsan (auth.)
- Tags: Non-associative Rings and Algebras, Probability Theory and Stochastic Processes, Partial Differential Equations, Systems Theory Control, Applications of Mathematics
- Series: Mathematics and Its Applications 466
- Year: 1999
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-x
Introduction....Pages 1-4
Gradient Systems in a Lie Algebra....Pages 5-23
Representation of a Gradient System....Pages 25-48
Finitely Generated over Orbits Lie Algebras and Algebraic Representation of the Gradient System....Pages 49-75
Applications....Pages 77-115
Stabilization and Related Problems....Pages 117-195
Back Matter....Pages 197-243
Content:
Front Matter....Pages i-x
Introduction....Pages 1-4
Gradient Systems in a Lie Algebra....Pages 5-23
Representation of a Gradient System....Pages 25-48
Finitely Generated over Orbits Lie Algebras and Algebraic Representation of the Gradient System....Pages 49-75
Applications....Pages 77-115
Stabilization and Related Problems....Pages 117-195
Back Matter....Pages 197-243
....