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Global Analysis in Mathematical Physics

Geometric and Stochastic Methods

  • Yuri Gliklikh

Part of the Applied Mathematical Sciences book series (AMS, volume 122)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Finite-Dimensional Differential Geometry and Mechanics

    1. Front Matter
      Pages 1-1
    2. Yuri Gliklikh
      Pages 17-35
    3. Yuri Gliklikh
      Pages 39-46
  3. Stochastic Differential Geometry and its Applications to Physics

    1. Front Matter
      Pages 47-47
    2. Yuri Gliklikh
      Pages 87-94
  4. Infinite-Dimensional Differential Geometry and Hydrodynamics

  5. Back Matter
    Pages 179-216

About this book

Introduction

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 Sections 19 and 20. I am grateful to Viktor L. Ginzburg for his hard work on the transla­ tion and for writing Appendix F, and to Tomasz Zastawniak for his numerous suggestions. My special thanks go to the referee for his valuable remarks on the theory of stochastic processes. Finally, I would like to acknowledge the support of the AMS fSU Aid Fund and the International Science Foundation (Grant NZBOOO), which made possible my work on some of the new results included in the English edition of the book. Voronezh, Russia Yuri Gliklikh September, 1995 Preface to the Russian Edition The present book is apparently the first in monographic literature in which a common treatment is given to three areas of global analysis previously consid­ ered quite distant from each other, namely, differential geometry and classical mechanics, stochastic differential geometry and statistical and quantum me­ chanics, and infinite-dimensional differential geometry of groups of diffeomor­ phisms and hydrodynamics. The unification of these topics under the cover of one book appears, however, quite natural, since the exposition is based on a geometrically invariant form of the Newton equation and its analogs taken as a fundamental law of motion.

Keywords

Christoffel symbols Martingale Semimartingale Stochastic processes classical mechanics diffeomorphism differential geometry manifold mathematical physics stochastic process

Authors and affiliations

  • Yuri Gliklikh
    • 1
  1. 1.Department of MathematicsVoronezh State UniversityVoronezhRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1866-1
  • Copyright Information Springer-Verlag New York, Inc. 1997
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7317-2
  • Online ISBN 978-1-4612-1866-1
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site