Global Analysis in Mathematical Physics Geometric and Stochastic Methods
The first edition of this book entitled Analysis on Riemannian Manifolds and Some Problems of Mathematical Physics was published by Voronezh Univer sity Press in 1989. For its English edition, the book has been substantially revised and expanded. In particular, new material has been added to Sectio...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1997, 1997
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| Edition: | 1st ed. 1997 |
| Series: | Applied Mathematical Sciences
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| Subjects: | |
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| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I. Finite-Dimensional Differential Geometry and Mechanics
- 1 Some Geometric Constructions in Calculus on Manifolds
- 2 Geometric Formalism of Newtonian Mechanics
- 3 Accessible Points of Mechanical Systems
- II. Stochastic Differential Geometry and its Applications to Physics
- 4 Stochastic Differential Equations on Riemannian Manifolds
- 5 The Langevin Equation
- 6 Mean Derivatives, Nelson’s Stochastic Mechanics, and Quantization
- III. Infinite-Dimensional Differential Geometry and Hydrodynamics
- 7 Geometry of Manifolds of Diffeomorphisms
- 8 Lagrangian Formalism of Hydrodynamics of an Ideal Incompressible Fluid
- 9 Hydrodynamics of a Viscous Incompressible Fluid and Stochastic Differential Geometry of Groups of Diffeomorphisms
- Appendices
- A. Introduction to the Theory of Connections
- Connections on Principal Bundles
- Connections on the Tangent Bundle
- Covariant Derivatives
- Connection Coefficients and Christoffel Symbols
- Second-Order Differential Equations and the Spray
- The Exponential Map and Normal Charts
- B. Introduction to the Theory of Set-Valued Maps
- C. Basic Definitions of Probability Theory and the Theory of Stochastic Processes
- Stochastic Processes and Cylinder Sets
- The Conditional Expectation
- Markovian Processes
- Martingales and Semimartingales
- D. The Itô Group and the Principal Itô Bundle
- E. Sobolev Spaces
- F. Accessible Points and Closed Trajectories of Mechanical Systems (by Viktor L. Ginzburg)
- Growth of the Force Field and Accessible Points
- Accessible Points in Systems with Constraints
- Closed Trajectories of Mechanical Systems
- References