Global Analysis in Mathematical Physics: Geometric and Stochastic Methods: Applied Mathematical Sciences, cartea 122
Autor Yuri Gliklikh Traducere de V. L. Ginzburgen Limba Engleză Hardback – 13 dec 1996
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Specificații
ISBN-13: 9780387948676
ISBN-10: 0387948678
Pagini: 236
Ilustrații: XV, 216 p.
Dimensiuni: 155 x 235 x 18 mm
Greutate: 0.49 kg
Ediția:1997
Editura: Springer
Colecția Springer
Seria Applied Mathematical Sciences
Locul publicării:New York, NY, United States
ISBN-10: 0387948678
Pagini: 236
Ilustrații: XV, 216 p.
Dimensiuni: 155 x 235 x 18 mm
Greutate: 0.49 kg
Ediția:1997
Editura: Springer
Colecția Springer
Seria Applied Mathematical Sciences
Locul publicării:New York, NY, United States
Public țintă
ResearchCuprins
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.