Bücher der Reihe Lecture Notes in Mathematics

This volume of proceedings contains selected and refereed articles - both surveys and original research articles - on geometric structures, global analysis, differential operators on manifolds, cohomology theories and other topics in differential geometry.

Cohomology of arithmetic groups serves as a tool in studying possible relations between the theory of automorphic forms and the arithmetic of algebraic varieties resp. the geometry of locally symmetric spaces. These proceedings will serve as a guide to this still rapidly developing area of mathematics. Besides two survey articles, the contributions are original research papers.

Before his untimely death in 1986, Alain Durand had undertaken a systematic and in-depth study of the arithmetic perspectives of polynomials. Four unpublished articles of his, formed the centerpiece of attention at a colloquium in Paris in 1988 and are reproduced in this volume together with 11 other papers on closely related topics. A detailed introduction by M. Langevin sets the scene and places these articles in a unified perspective.

Kyoto, Japan, 1972

Proceedings 1972

A workshop on Singularities, Bifuraction and Dynamics was held at Warwick in July 1989, as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory and applications in the sciences. The papers are original research, stimulated by the symposium and workshop: All have been refereed and none will appear elsewhere. The main topic of volume II is new methods for the study of bifurcations in nonlinear dynamical systems, and applications of these.

Proceedings of a Conference held in Heidelberg, September 10 - 14, 1984

A workshop on Singularities, Bifurcation and Dynamics was held at Warwick in July 1989 as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory, and applications in the sciences. The papers are orginal research, stimulated by the symposium and workshops: All have been refereed, and none will appear elsewhere. The main topic, deformation theory, is represented by several papers on descriptions of the bases of versal deformations, and several more on descriptions of the generic fibres. Other topics include stratifications, and applications to differential geometry.

The purpose of the conference was to represent recentdevelopments in measure theoretic, differentiable andtopological dynamical systems as well as connections toprobability theory, stochastic processes, operator theoryand statistical physics. Only original research papers thatdo not appear elsewhere are included in the proceedings. Their topics include: C(2)-diffeomorphisms of compactRiemann manifolds, geodesic flows, chaotic behaviour inbillards, nonlinear ergodic theory, central limit theoremsfor subadditive processes, Hausdorff measures for parabolicrational maps, Markov operators, periods of cycles, Juliasets, ergodic theorems. From the Contents: L.A. Bunimovich: On absolutely focusingmirrors.- M. Denker, M. Urbanski: The dichotomy of Hausdorffmeasures and equilibrium states for parabolic rationalmaps.- F. Ledrappier: Ergodic properties of the stablefoliations.- U. Wacker: Invariance principles and centrallimit theorems for nonadditive stationary processes.- J. Schmeling, R. Siegmund-Schultze: Hoelder continuity of theholonomy map for hyperbolic basic sets.- A.M. Blokh: Thespectral decomposition, periods of cycles and Misiurewiczconjecture for graph maps.-and contributions by Chr. Bandt and K. Keller, T. Bogenschutz andH. Crauel, H.G. Bothe, M. Denker and K.F. Kramer, T.P. Hill and U. Krengel, A. Iwanik, Z.S. Kowalski,E. Lesigne, J. Malczak, I. Mizera, J. Sipos, R. Wittmann.

With contributions by numerous experts

The central theme of this volume is commutative algebra, with emphasis on special graded algebras, which are increasingly of interest in problems of algebraic geometry, combinatorics and computer algebra. Most of the papers have partly survey character, but are research-oriented, aiming at classification and structural results.

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.

The Nordic Summer School 1985 presented to young researchers the mathematical aspects of the ongoing research stemming from the study of field theories in physics and the differential geometry of fibre bundles in mathematics. The volume includes papers, often with original lines of attack, on twistor methods for harmonic maps, the differential geometric aspects of Yang-Mills theory, complex differential geometry, metric differential geometry and partial differential equations in differential geometry. Most of the papers are of lasting value and provide a good introduction to their subject.

About ten years ago, V.D. Goppa found a surprisingconnection between the theory of algebraic curves over afinite field and error-correcting codes. The aim of themeeting "e;Algebraic Geometry and Coding Theory"e; was to give asurvey on the present state of research in this field andrelated topics. The proceedings contain research papers onseveral aspects of the theory, among them: Codes constructedfrom special curves and from higher-dimensional varieties,Decoding of algebraic geometric codes, Trace codes, Exponen-tial sums, Fast multiplication in finite fields, Asymptoticnumber of points on algebraic curves, Sphere packings.