Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations
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. Howeve...
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| Format: | eBook |
| Language: | English |
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Dordrecht
Springer Netherlands
1999, 1999
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| Edition: | 1st ed. 1999 |
| Series: | Mathematics and Its Applications
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Gradient Systems in a Lie Algebra
- 1.1 Preliminaries
- 1.2 Gradient systems in Fn and Der (Rn)
- 1.3 Gradient Systems Determined by a Lie Algebra
- 2 Representation of a Gradient System
- 2.1 Finite-Dimensional Lie Algebra
- 2.2 The Maximal Rank Lie Algebra
- 2.3 Integral Manifolds
- 2.4 Some applications
- 3 F. G. O. Lie Algebras
- 3.1 Lie algebras finitely generated over orbits
- 3.2 Nonsingularity of the gradient system
- 3.3 Some Applications
- 4 Applications
- 4.1 Systems of Semiliniar Equations
- 4.2 Stochastic Differential Equations
- 4.3 Systems of Hyperbolic equations
- 4.4 Finite-Dimensional Nonlinear Filters
- 4.5 Affine Control Systems
- 4.6 Integral Representation of Solutions
- 4.7 Decomposition of affine control systems
- 5 Stabilization and Related Problems
- 5.1 Equivalent Controllable Systems
- 5.2 Approximations, Small Controls
- 5.3 Nonlinear Control Systems
- 5.4 Stabilization of Affine Control Systems
- 5.5 Controlled Invariant Lie Algebras
- 5.6 Stochastic differential equations