Mapping Degree Theory
Author: Enrique Outerelo Domínguez
Publisher:
Published: 2009
Total Pages: 258
ISBN-13: 9781470411718
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Mapping Degree Theory
Author: Enrique Outerelo
Publisher: American Mathematical Soc.
Published: 2009-11-12
Total Pages: 258
ISBN-13: 0821849158
DOWNLOAD EBOOKThis 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.
Topological Degree Theory and Applications
Author: Yeol Je Cho
Publisher: CRC Press
Published: 2006-03-27
Total Pages: 228
ISBN-13: 1420011480
DOWNLOAD EBOOKSince 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
Degree Theory in Analysis and Applications
Author: Irene Fonseca
Publisher: Oxford University Press
Published: 1995
Total Pages: 226
ISBN-13: 9780198511960
DOWNLOAD EBOOKThis 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.
Degree Theory of Immersed Hypersurfaces
Author: Harold Rosenberg
Publisher: American Mathematical Soc.
Published: 2020-09-28
Total Pages: 62
ISBN-13: 1470441853
DOWNLOAD EBOOKThe 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.
Degree Theory for Equivariant Maps, the General $S^1$-Action
Author: Jorge Ize
Publisher: American Mathematical Soc.
Published: 1992
Total Pages: 194
ISBN-13: 0821825429
DOWNLOAD EBOOKIn 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.
Geometric Methods in Degree Theory for Equivariant Maps
Author: Alexander M. Kushkuley
Publisher: Lecture Notes in Mathematics
Published: 1996-08-19
Total Pages: 152
ISBN-13:
DOWNLOAD EBOOKThe 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.
Topological Degree Methods in Nonlinear Boundary Value Problems
Author: J. Mawhin
Publisher: American Mathematical Soc.
Published: 1979
Total Pages: 130
ISBN-13: 082181690X
DOWNLOAD EBOOKContains 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.
A Topological Introduction to Nonlinear Analysis
Author: Robert F. Brown
Publisher: Springer
Published: 2014-11-27
Total Pages: 229
ISBN-13: 3319117947
DOWNLOAD EBOOKThis 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)
Topological and Approximation Methods of Degree Theory of Set-valued Maps
Author: Wojciech Kryszewski
Publisher:
Published: 1994
Total Pages: 112
ISBN-13:
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