Global and stochastic analysis with applications to mathematical physics / Yuri E. Gliklikh.

Format:

Book

Author/Creator:

Gliklikh, I︠U︡. E.

Series:

Theoretical and mathematical physics (Springer (Firm))

Theoretical and mathematical physics

Language:

English

Subjects (All):

Global analysis (Mathematics).

Mathematical physics.

Physical Description:

1 online resource (453 p.)

Edition:

1st ed. 2011.

Place of Publication:

London : Springer-Verlag, 2010.

Language Note:

English

Summary:

Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics.

Contents:

Part I Global Analysis

Manifolds and Related Objects

Connections

Ordinary Differential Equations

Elements of the Theory of Set-Valued Mappings

Analysis on Groups of Diffeomorphisms

Part II Stochastic Analysis

Essentials from Stochastic Analysis in Linear Spaces

Stochastic Analysis on Manifolds

Mean Derivatives in Linear Spaces

Mean Derivatives on Manifolds

Stochastic Analysis on Groups of Diffeomorphism

Part III Applications to Mathematical Physics

Newtonian Mechanics

Accessible Points and Sub-Manifolds of Mechanical Systems. Controllability

Some Problems on Lorentz Manifolds

Mechanical Systems with Random Perturbations

The Newton-Nelson Equation

Hydrodynamics.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-283-08824-X

9786613088246

0-85729-163-7

OCLC:

700167299