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Variétés différentielles et analytiques Fascicule de résultats Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce fascicule rassemble les notions fondamentales et les principaux résultats de la théorie des variétés différentiables (sur le corps des nombres réels) et des variétés analytiques (sur un corps value complet non discret). Il ne contient pas de démonstration. Ce volume est une réimpression des éditions de 1967 et 1971.

Differential geometry. Global analysis --- differentiaal geometrie

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This self-contained treatment of Morse Theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinct parts. The first part contains the foundations of Morse theory (over the reals). The second part consists of applications of Morse theory over the reals, while the last part describes the basics and some applications of complex Morse theory, a.k.a. Picard-Lefschetz theory. This is the first textbook to include topics such as Morse-Smale flows, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The exposition is enhanced with examples, problems, and illustrations, and will be of interest to graduate students as well as researchers. The reader is expected to have some familiarity with cohomology theory and with the differential and integral calculus on smooth manifolds. Liviu Nicolaescu is Associate Professor of Mathematics at University of Notre Dame.

Differential geometry. Global analysis --- Differential topology --- differentiaal geometrie --- topologie

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The book presents constructive methods of symbolic dynamics and their applications to the study of continuous and discrete dynamical systems. The main idea is the construction of a directed graph which represents the str- ture of the state space for the investigated dynamical system. The book c- tains a su?cient number of examples of concrete dynamical systems from illustrative ones to systems of current interest. Results of their numerical s- ulations with detailed comments are presented. For an understanding of the book matter, it is su?cient to be acquainted with a general course of ordinary di?erential equations. The new theoretical results are presented with proofs; the most attention is given to their applications. The book is designed for - niorstudentsandresearchesengagedinapplications ofthedynamicalsystems theory. The base of the presented book is the course of lectures given during the YouthWorkshopComputerModelingofDynamicalSystems (June2004,St. Petersburg) initiated and supported by the UNESCO-ROSTE. Parts of these lectures were presented in ETH, Zurich, 1992; Pohang University of Techn- ogy, South Korea, 1993; Belmont University, USA, 1996; St. Petersburg U- versity, Russia, 1999; Suleyman Demirel University, Turkey, 2000; Augsburg University, Germany, 2001; Kalmer University, Sweden, 2004. Symbolic image, coding, pseudo-orbit, shadowing property, Newton method, attractor, ?ltration, structural graph, entropy, projective space, L- punov exponent, Morse spectrum, hyperbolicity, structural stability, contr- lability, invariant manifold, chaos.

Differential geometry. Global analysis --- Differential equations --- Numerical analysis --- differentiaalvergelijkingen --- differentiaal geometrie --- numerieke analyse

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Algebra --- Differential geometry. Global analysis --- Partial differential equations --- Mathematical physics --- differentiaalvergelijkingen --- algebra --- differentiaal geometrie --- wiskunde --- fysica

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The São Carlos Workshop on Real and Complex Singularities is the longest running workshop in singularities. It is held every two years and is a key international event for people working in the field. This volume contains papers presented at the eighth workshop, held at the IML, Marseille, July 19-23, 2004. The workshop offers the opportunity to establish the state of the art and to present new trends, new ideas and new results in all of the branches of singularities. This is reflected by the contributions in this book. The main topics discussed are equisingularity of sets and mappings, geometry of singular complex analytic sets, singularities of mappings, characteristic classes, classification of singularities, interaction of singularity theory with some of the new ideas in algebraic geometry imported from theoretical physics, and applications of singularity theory to geometry of surfaces in low dimensional euclidean spaces, to differential equations and to bifurcation theory.

Differential geometry. Global analysis --- Differential topology --- Geometry --- Ergodic theory. Information theory --- differentiaal geometrie --- geometrie --- topologie --- informatietheorie