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Author : Enrique Outerelo Domínguez
Publisher :
ISBN 13 : 9781470411718
Total Pages : 258 pages
Book Rating : 4.4/5 (117 download)
Download or read book Mapping Degree Theory written by Enrique Outerelo Domínguez and published by . This book was released on 2009 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Enrique Outerelo
Publisher : American Mathematical Soc.
ISBN 13 : 0821849158
Total Pages : 258 pages
Book Rating : 4.8/5 (218 download)
Download or read book Mapping Degree Theory written by Enrique Outerelo and published by American Mathematical Soc.. This book was released on 2009-11-12 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Yeol Je Cho
Publisher : CRC Press
ISBN 13 : 1420011480
Total Pages : 228 pages
Book Rating : 4.4/5 (2 download)
Download or read book Topological Degree Theory and Applications written by Yeol Je Cho and published by CRC Press. This book was released on 2006-03-27 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the 1960s, many researchers have extended topological degree theory to various non-compact type nonlinear mappings, and it has become a valuable tool in nonlinear analysis. Presenting a survey of advances made in generalizations of degree theory during the past decade, this book focuses on topological degree theory in normed spaces and its ap
Author : Harold Rosenberg
Publisher : American Mathematical Soc.
ISBN 13 : 1470441853
Total Pages : 62 pages
Book Rating : 4.4/5 (74 download)
Download or read book Degree Theory of Immersed Hypersurfaces written by Harold Rosenberg and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Irene Fonseca
Publisher : Oxford University Press
ISBN 13 : 9780198511960
Total Pages : 226 pages
Book Rating : 4.5/5 (119 download)
Download or read book Degree Theory in Analysis and Applications written by Irene Fonseca and published by Oxford University Press. This book was released on 1995 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text examines degree theory and some of its applications in analysis. Topics described include: degree theory for continuous functions; the multiplication theorem; Hopf's theorem; Brower's fixed point theorem; odd mappings; and Jordan's separation theorem.
Author : Jorge Ize
Publisher : American Mathematical Soc.
ISBN 13 : 0821825429
Total Pages : 194 pages
Book Rating : 4.8/5 (218 download)
Download or read book Degree Theory for Equivariant Maps, the General $S^1$-Action written by Jorge Ize and published by American Mathematical Soc.. This book was released on 1992 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we consider general [italic]S1-actions, which may differ on the domain and on the range, with isotropy subspaces with one dimension more on the domain. In the special case of self-maps the [italic]S1-degree is given by the usual degree of the invariant part, while for one parameter [italic]S1-maps one has an integer for each isotropy subgroup different from [italic]S1. In particular we recover all the [italic]S1-degrees introduced in special cases by other authors and we are also able to interpret period doubling results on the basis of our [italic]S1-degree. The applications concern essentially periodic solutions of ordinary differential equations.
Author : Alexander M. Kushkuley
Publisher : Lecture Notes in Mathematics
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.F/5 ( download)
Download or read book Geometric Methods in Degree Theory for Equivariant Maps written by Alexander M. Kushkuley and published by Lecture Notes in Mathematics. This book was released on 1996-08-19 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : J. Mawhin
Publisher : American Mathematical Soc.
ISBN 13 : 082181690X
Total Pages : 130 pages
Book Rating : 4.8/5 (218 download)
Download or read book Topological Degree Methods in Nonlinear Boundary Value Problems written by J. Mawhin and published by American Mathematical Soc.. This book was released on 1979 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains lectures from the CBMS Regional Conference held at Harvey Mudd College, June 1977. This monograph consists of applications to nonlinear differential equations of the author's coincidental degree. It includes an bibliography covering many aspects of the modern theory of nonlinear differential equations and the theory of nonlinear analysis.
Author : Wojciech Kryszewski
Publisher :
ISBN 13 :
Total Pages : 112 pages
Book Rating : 4.3/5 (121 download)
Download or read book Topological and Approximation Methods of Degree Theory of Set-valued Maps written by Wojciech Kryszewski and published by . This book was released on 1994 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert F. Brown
Publisher : Springer
ISBN 13 : 3319117947
Total Pages : 229 pages
Book Rating : 4.3/5 (191 download)
Download or read book A Topological Introduction to Nonlinear Analysis written by Robert F. Brown and published by Springer. This book was released on 2014-11-27 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Wojciech Kryszewski
Publisher :
ISBN 13 :
Total Pages : 101 pages
Book Rating : 4.:/5 (15 download)
Download or read book Topological and Approximation Methods of Degree Theory of Set-valued Maps written by Wojciech Kryszewski and published by . This book was released on 1994 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wieslaw Krawcewicz
Publisher : Wiley-Interscience
ISBN 13 :
Total Pages : 400 pages
Book Rating : 4.3/5 (91 download)
Download or read book Theory of Degrees with Applications to Bifurcations and Differential Equations written by Wieslaw Krawcewicz and published by Wiley-Interscience. This book was released on 1997-02-05 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to degree theory and its applications to nonlinear differential equations. It uses an applications-oriented to address functional analysis, general topology and differential equations and offers a unified treatment of the classical Brouwer degree, the recently developed S?1-degree and the Dold-Ulrich degree for equivalent mappings and bifurcation problems. It integrates two seemingly disparate concepts, beginning with review material before shifting to classical theory and advanced application techniques.
Author : P. H. Rabinowitz
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (897 download)
Download or read book A Note on Topological Degree Theory for Hoomorphic Maps written by P. H. Rabinowitz and published by . This book was released on 1972 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Patrick M. Fitzpatrick
Publisher :
ISBN 13 :
Total Pages : 43 pages
Book Rating : 4.:/5 (883 download)
Download or read book Degree Theory for Proper C2-Fredholm Maps 1 written by Patrick M. Fitzpatrick and published by . This book was released on with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hemant Kumar Pathak
Publisher : Springer
ISBN 13 : 9811088667
Total Pages : 830 pages
Book Rating : 4.8/5 (11 download)
Download or read book An Introduction to Nonlinear Analysis and Fixed Point Theory written by Hemant Kumar Pathak and published by Springer. This book was released on 2018-05-19 with total page 830 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Patrick M. Fitzpatrick
Publisher :
ISBN 13 :
Total Pages : 33 pages
Book Rating : 4.:/5 (883 download)
Download or read book Degree Theory for Proper C2-Fredholm Maps 2 written by Patrick M. Fitzpatrick and published by . This book was released on with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kenneth O. Leland
Publisher :
ISBN 13 :
Total Pages : 73 pages
Book Rating : 4.:/5 (227 download)
Download or read book A Direct Approach to the Theory of the Degree of a Mapping written by Kenneth O. Leland and published by . This book was released on 1975 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expository paper revives an approach to the theory of the degree of a mapping from Euclidean n-space into Euclidean n-space of value to analysts and applied mathematicians that has been obscured by the explosive growth of recent years. This approach can be called that of singular homology, a field which has been eclipsed by the rise of simplicial homology and its many generalizations.
