Global Analysis in Mathematical Physics

Geometric and Stochastic Methods

AvYuri Gliklikh

Inbunden, Engelska, 1996

Del i serien Applied Mathematical Sciences

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Beskrivning

This book gives a common treatment to three areas of application of Global analysis to Mathematical Physics previously considered quite distant from each other. These areas are the geometry of manifolds applied to classical mechanics, stochastic differential geometry used in quantum and statistical mechanics, and infinite-dimensional differential geometry fundamental for hydrodynamics.

Produktinformation

Utgivningsdatum:1996-12-13
Mått:155 x 235 x 18 mm
Vikt:524 g
Format:Inbunden
Språk:Engelska
Serie:Applied Mathematical Sciences
Antal sidor:216
Förlag:Springer-Verlag New York Inc.
ISBN:9780387948676
Översättare:V.L. Ginzburg, V. L. Ginzburg

Utforska kategorier

Topologi inom Naturvetenskap och teknik
Tillämpad matematik inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Innehållsförteckning

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.