Bøger af Yuri E. Gliklikh

The main aim of this book is to develop the methods of Global Analysis and of 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 quite distant from each other and requiring different methods of investigation. Among those areas we mention classical mechanics on non-linear configuration spaces, some problems of statistical and quantum physics, hydrodynamics, etc. The idea, yielding the unification of these topics, is based on the use of a geometrically invariant form of Newton's second law and its analogs (stochastic, set-valued, infinite-dimensional, etc.) as a fundamental equation of motion.

This volume (a sequel to LNM 1108, 1214, 1334 and 1453)continues the presentation to English speaking readers ofthe Voronezh University press series on Global Analysis andIts Applications. The papers are selected fromtwo Russianissues entitled "e;Algebraic questions of Analysis andTopology"e; and "e;Nonlinear Operators in Global Analysis"e;. CONTENTS: YuE. Gliklikh: Stochastic analysis, groups ofdiffeomorphisms and Lagrangian description of viscousincompressible fluid.- A.Ya. Helemskii: From topologicalhomology: algebras with different properties of homologicaltriviality.- V.V. Lychagin, L.V. Zil'bergleit: Duality instable Spencer cohomologies.- O.R. Musin: On some problemsof computational geometry and topology.- V.E. Nazaikinskii,B.Yu. Sternin, V.E.Shatalov: Introduction to Maslov'soperational method (non-commutative analysis anddifferential equations).- Yu.B. Rudyak: The problem ofrealization of homology classes from Poincare up to thepresent.- V.G. Zvyagin, N.M. Ratiner: Oriented degree ofFredholm maps of non-negativeindex and its applications toglobal bifurcation of solutions.- A.A. Bolibruch: Fuchsiansystems with reducible monodromy and the Riemann-Hilbertproblem.- I.V. Bronstein, A.Ya. Kopanskii: Finitely smoothnormal forms of vector fields in the vicinity of a restpoint.- B.D. Gel'man: Generalized degree of multi-valuedmappings.- G.N. Khimshiashvili: On Fredholmian aspects oflinear transmission problems.- A.S. Mishchenko: Stationarysolutions of nonlinear stochastic equations.- B.Yu. Sternin,V.E. Shatalov: Continuation of solutions to ellipticequations and localisation of singularities.- V.G. Zvyagin,V.T. Dmitrienko: Properness of nonlinear ellipticdifferential operators in H|lder spaces.

This text gives a common treatment to three areas of application of global analysis to mathematical physics: the geometry of manifolds applied to classical mechanics; stochastic differential geometry used in quantum and statistical mechanics; and infinites-dimensional differential geometry.

It deals with a lot of various second order differential equations on finite and infinite-dimensional manifolds arising in Physics, and its validity is based on the deep inter-relation between modem Differential Geometry and certain parts of the Theory of Stochastic Processes, discovered not so long ago.