Download or read book Equivariant Degree Theory written by Jorge Ize and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new degree theory for maps which commute with a group of symmetries. This degree is no longer a single integer but an element of the group of equivariant homotopy classes of maps between two spheres and depends on the orbit types of the spaces. The authors develop completely the theory and applications of this degree in a self-contained presentation starting with only elementary facts. The first chapter explains the basic tools of representation theory, homotopy theory and differential equations needed in the text. Then the degree is defined and its main abstract properties are derived. The next part is devoted to the study of equivariant homotopy groups of spheres and to the classification of equivariant maps in the case of abelian actions. These groups are explicitely computed and the effects of symmetry breaking, products and composition are thorougly studied. The last part deals with computations of the equivariant index of an isolated orbit and of an isolated loop of stationary points. Here differential equations in a variety of situations are considered: symmetry breaking, forcing, period doubling, twisted orbits, first integrals, gradients etc. Periodic solutions of Hamiltonian systems, in particular spring-pendulum systems, are studied as well as Hopf bifurcation for all these situations.
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.
Download or read book Degree Theory for Equivariant Maps written by Jorge Ize and published by Oxford University Press, USA. This book was released on 2014-08-31 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is devoted to a detailed study of the equivariant degree and its applications for the case of an S ]1-action. This degree is an element of the equivariant homotopy group of spheres, which are computed in step-by-step extension process. Applications include the index of an isolated orbit, branching and Hopf bifurcation, and period doubling and symmetry breaking for systems of autonomous differential equations. The authors have paid special attention to making the text as self-contained as possible, so that the only background required is some familiarity with the basic ideas of homotopy theory and of Floquet theory in differential equations. Illustrating in a natural way the interplay between topology and analysis, this book will be of interest to researchers and graduate students.
Download or read book Geometric Methods in Degree Theory for Equivariant Maps written by Alexander M. Kushkuley and published by Springer. This book was released on 2006-11-14 with total page 143 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.
Download or read book Geometric Methods in Degree Theory for Equivariant Maps written by Alexander M. Kushkuley and published by . This book was released on 2014-01-15 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Equivariant Degree Theory for Networked Dynamical Systems written by Haibo Ruan and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Applied Equivariant Degree written by Zalman Balanov and published by . This book was released on 2006 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Equivariant Degree with Symmetric Nonlinear Boundary Value Problems written by My Linh Nguyen and published by LAP Lambert Academic Publishing. This book was released on 2014-07-03 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Boundary value/periodic problems for the nonlinear equation (or, more generally, second order nonlinear ODEs) have been the focus of nonlinear analysis study for a long time. The goal of this book is to show how the equivariant degree theory can be used for the systematic study of multiple solutions to several (symmetric) generalizations of BVP and for the classification of symmetric properties of these solutions. There are several classical methods of nonlinear analysis used to solve the BVP. However, their application encounters serious difficulties if: the group of symmetries is large, the dimension of the problem is high, and multiplicities of eigenvalues of linearizations are large, etc. In this book, we: (i) set up the abstract functional analysis framework for studying symmetric properties of multiple solutions to symmetric generalizations of the BV problem via the equivariant degree approach; (ii) describe wide classes of second order BVPs admitting dihedral symmetries to which the abstract theory can be effectively applied; (iii) and apply the obtained results to several classes of implicit second order symmetric differential equations.
Download or read book Fixed Point Theory written by Andrzej Granas and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Fixed Points is one of the most powerful tools of modern mathematics. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications. From the reviews: "I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis." --MATHEMATICAL REVIEWS
Download or read book Handbook of Topological Fixed Point Theory written by Robert F. Brown and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 966 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first in the world literature presenting all new trends in topological fixed point theory. Until now all books connected to the topological fixed point theory were devoted only to some parts of this theory. This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.
Download or read book S1 equivariant Degree and Global Bifurcation Theory for Condensing Fields and Neutral Equations written by Wiesław Krawcewicz and published by . This book was released on 1991 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem written by Michael A. Hill and published by Cambridge University Press. This book was released on 2021-07-29 with total page 881 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.
Download or read book Equivariant Homotopy and Cohomology Theory written by J. Peter May and published by American Mathematical Soc.. This book was released on 1996 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.
Download or read book Topological Nonlinear Analysis II written by Michele Matzeu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in nonlin ear analysis during the last three decades. It is intended, at least partly, as a continuation of Topological Nonlinear Analysis: Degree, Singularity and Varia tions, published in 1995. The survey articles presented are concerned with three main streams of research, that is topological degree, singularity theory and variational methods, They reflect the personal taste of the authors, all of them well known and distinguished specialists. A common feature of these articles is to start with a historical introduction and conclude with recent results, giving a dynamic picture of the state of the art on these topics. Let us mention the fact that most of the materials in this book were pre sented by the authors at the "Second Topological Analysis Workshop on Degree, Singularity and Variations: Developments of the Last 25 Years," held in June 1995 at Villa Tuscolana, Frascati, near Rome. Michele Matzeu Alfonso Vignoli Editors Topological Nonlinear Analysis II Degree, Singularity and Variations Classical Solutions for a Perturbed N-Body System Gianfausto Dell 'A ntonio O. Introduction In this review I shall consider the perturbed N-body system, i.e., a system composed of N point bodies of masses ml, ... mN, described in cartesian co ordinates by the system of equations (0.1) where f) V'k,m == -£l--' m = 1, 2, 3.
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.
