Mapping Degree Theory
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Author | : Enrique Outerelo |
Publisher | : American Mathematical Soc. |
Total Pages | : 258 |
Release | : 2009-11-12 |
Genre | : Mathematics |
ISBN | : 0821849158 |
This textbook treats the classical parts of mapping degree theory, with a detailed account of its history traced back to the first half of the 18th century. After a historical first chapter, the remaining four chapters develop the mathematics. An effort is made to use only elementary methods, resulting in a self-contained presentation. Even so, the book arrives at some truly outstanding theorems: the classification of homotopy classes for spheres and the Poincare-Hopf Index Theorem, as well as the proofs of the original formulations by Cauchy, Poincare, and others. Although the mapping degree theory you will discover in this book is a classical subject, the treatment is refreshing for its simple and direct style. The straightforward exposition is accented by the appearance of several uncommon topics: tubular neighborhoods without metrics, differences between class 1 and class 2 mappings, Jordan Separation with neither compactness nor cohomology, explicit constructions of homotopy classes of spheres, and the direct computation of the Hopf invariant of the first Hopf fibration. The book is suitable for a one-semester graduate course. There are 180 exercises and problems of different scope and difficulty.
Author | : Harold Rosenberg |
Publisher | : American Mathematical Soc. |
Total Pages | : 62 |
Release | : 2020-09-28 |
Genre | : Mathematics |
ISBN | : 1470441853 |
The authors develop a degree theory for compact immersed hypersurfaces of prescribed $K$-curvature immersed in a compact, orientable Riemannian manifold, where $K$ is any elliptic curvature function.
Author | : Alexander M. Kushkuley |
Publisher | : Lecture Notes in Mathematics |
Total Pages | : 152 |
Release | : 1996-08-19 |
Genre | : Mathematics |
ISBN | : |
The book introduces conceptually simple geometric ideas based on the existence of fundamental domains for metric G- spaces. A list of the problems discussed includes Borsuk-Ulam type theorems for degrees of equivariant maps in finite and infinite dimensional cases, extensions of equivariant maps and equivariant homotopy classification, genus and G-category, elliptic boundary value problem, equivalence of p-group representations. The new results and geometric clarification of several known theorems presented here will make it interesting and useful for specialists in equivariant topology and its applications to non-linear analysis and representation theory.
Author | : Wojciech Kryszewski |
Publisher | : |
Total Pages | : 112 |
Release | : 1994 |
Genre | : Approximation theory |
ISBN | : |
Author | : Robert F. Brown |
Publisher | : Springer |
Total Pages | : 229 |
Release | : 2014-11-27 |
Genre | : Mathematics |
ISBN | : 3319117947 |
This third edition is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully-expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world. Included in this new edition are several new chapters that present the fixed point index and its applications. The exposition and mathematical content is improved throughout. This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply focused and highly readable view of nonlinear analysis by a practicing topologist who has seen a clear path to understanding. "For the topology-minded reader, the book indeed has a lot to offer: written in a very personal, eloquent and instructive style it makes one of the highlights of nonlinear analysis accessible to a wide audience."-Monatshefte fur Mathematik (2006)
Author | : Hemant Kumar Pathak |
Publisher | : Springer |
Total Pages | : 830 |
Release | : 2018-05-19 |
Genre | : Mathematics |
ISBN | : 9811088667 |
This book systematically introduces the theory of nonlinear analysis, providing an overview of topics such as geometry of Banach spaces, differential calculus in Banach spaces, monotone operators, and fixed point theorems. It also discusses degree theory, nonlinear matrix equations, control theory, differential and integral equations, and inclusions. The book presents surjectivity theorems, variational inequalities, stochastic game theory and mathematical biology, along with a large number of applications of these theories in various other disciplines. Nonlinear analysis is characterised by its applications in numerous interdisciplinary fields, ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to stochastic game theory. Organised into ten chapters, the book shows the elegance of the subject and its deep-rooted concepts and techniques, which provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in diverse applied fields. It is intended for graduate and undergraduate students of mathematics and engineering who are familiar with discrete mathematical structures, differential and integral equations, operator theory, measure theory, Banach and Hilbert spaces, locally convex topological vector spaces, and linear functional analysis.
Author | : Enrique Outerelo Domínguez |
Publisher | : |
Total Pages | : 258 |
Release | : 2009 |
Genre | : Mappings (Mathematics) |
ISBN | : 9781470411718 |
Author | : Lech Górniewicz |
Publisher | : Springer Science & Business Media |
Total Pages | : 424 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 9780792360018 |
This volume presents a broad introduction to the topological fixed point theory of multivalued (set-valued) mappings, treating both classical concepts as well as modern techniques. A variety of up-to-date results is described within a unified framework.
Author | : Kung Ching Chang |
Publisher | : Springer Science & Business Media |
Total Pages | : 462 |
Release | : 2005-08-26 |
Genre | : Mathematics |
ISBN | : 9783540241331 |
This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It reviews the basic theories and methods, with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications, and provides the necessary preparation for almost all important aspects in contemporary studies. All methods are illustrated by carefully chosen examples from mechanics, physics, engineering and geometry.
Author | : Mohamed A. Khamsi |
Publisher | : John Wiley & Sons |
Total Pages | : 318 |
Release | : 2011-10-14 |
Genre | : Mathematics |
ISBN | : 1118031326 |
Diese Einfuhrung in das Gebiet der metrischen Raume richtet sich in erster Linie nicht an Spezialisten, sondern an Anwender der Methode aus den verschiedensten Bereichen der Naturwissenschaften. Besonders ausfuhrlich und anschaulich werden die Grundlagen von metrischen Raumen und Banach-Raumen erklart, Anhange enthalten Informationen zu verschiedenen Schlusselkonzepten der Mengentheorie (Zornsches Lemma, Tychonov-Theorem, transfinite Induktion usw.). Die hinteren Kapitel des Buches beschaftigen sich mit fortgeschritteneren Themen.