Author | Gliklikh, Yuri. author |
---|---|
Title | Global Analysis in Mathematical Physics [electronic resource] : Geometric and Stochastic Methods / by Yuri Gliklikh |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1997 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1866-1 |
Descript | XV, 216 p. online resource |
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, Nelsonโs 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 Itรด Group and the Principal Itรด 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