Homogeneous spaces and the Riccati equation in the calculus of variations
Author(s)
Bibliographic Information
Homogeneous spaces and the Riccati equation in the calculus of variations
（Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 86 . Control theory and optimization ; 1）
Springer, c2000
- Other Title
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Odnorodnye Prostranstva i uravnenie rikkati v variatsionnom ischislenii
Available at 103 libraries
Note
Originally published: Moscow : Faktorial, 1998
Bibliography: p. [276]-281
Includes index
Description and Table of Contents
Description
The only monograph on the topic, this book concerns geometric methods in the theory of differential equations with quadratic right-hand sides, closely related to the calculus of variations and optimal control theory. Based on the author's lectures, the book is addressed to undergraduate and graduate students, and scientific researchers.
Table of Contents
1. Classical Calculus of Variations.- 2. Riccati Equation in the Classical Calculus of Variations.- 3. Lie Groups and Lie Algebras.- 4. Grassmann Manifolds.- 5. Matrix Double Ratio.- 6. Complex Riccati Equations.- 7. Higher-Dimensional Calculus of Variations.- 8. On the Quadratic System of Partial Differential Equations Related to the Minimization Problem for a Multiple Integral.- Epilogue.- Appendix to the English Edition.- References.
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