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Topological Methods for Variational Problems with Symmetries

2006-11-15 Mathematics
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Release : 2006-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 994/5 ( reviews)

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Book Synopsis Topological Methods for Variational Problems with Symmetries by : Thomas Bartsch

Download or read book Topological Methods for Variational Problems with Symmetries written by Thomas Bartsch. This book was released on 2006-11-15. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry has a strong impact on the number and shape of solutions to variational problems. This has been observed, for instance, in the search for periodic solutions of Hamiltonian systems or of the nonlinear wave equation; when one is interested in elliptic equations on symmetric domains or in the corresponding semiflows; and when one is looking for "special" solutions of these problems. This book is concerned with Lusternik-Schnirelmann theory and Morse-Conley theory for group invariant functionals. These topological methods are developed in detail with new calculations of the equivariant Lusternik-Schnirelmann category and versions of the Borsuk-Ulam theorem for very general classes of symmetry groups. The Morse-Conley theory is applied to bifurcation problems, in particular to the bifurcation of steady states and hetero-clinic orbits of O(3)-symmetric flows; and to the existence of periodic solutions nearequilibria of symmetric Hamiltonian systems. Some familiarity with the usualminimax theory and basic algebraic topology is assumed.

Harmonic Maps and Minimal Immersions with Symmetries

1993 Mathematics
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Release : 1993
Genre : Mathematics
Kind : eBook
Book Rating : 498/5 ( reviews)

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Book Synopsis Harmonic Maps and Minimal Immersions with Symmetries by : James Eells

Download or read book Harmonic Maps and Minimal Immersions with Symmetries written by James Eells. This book was released on 1993. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.

Harmonic Maps and Minimal Immersions with Symmetries (AM-130), Volume 130

2016-03-02 Mathematics
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Release : 2016-03-02
Genre : Mathematics
Kind : eBook
Book Rating : 508/5 ( reviews)

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Book Synopsis Harmonic Maps and Minimal Immersions with Symmetries (AM-130), Volume 130 by : James Eells

Download or read book Harmonic Maps and Minimal Immersions with Symmetries (AM-130), Volume 130 written by James Eells. This book was released on 2016-03-02. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.

Topological Nonlinear Analysis

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 701/5 ( reviews)

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Book Synopsis Topological Nonlinear Analysis by : Michele Matzeu

Download or read book Topological Nonlinear Analysis written by Michele Matzeu. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Topological tools in Nonlinear Analysis had a tremendous develop ment during the last few decades. The three main streams of research in this field, Topological Degree, Singularity Theory and Variational Meth ods, have lately become impetuous rivers of scientific investigation. The process is still going on and the achievements in this area are spectacular. A most promising and rapidly developing field of research is the study of the role that symmetries play in nonlinear problems. Symmetries appear in a quite natural way in many problems in physics and in differential or symplectic geometry, such as closed orbits for autonomous Hamiltonian systems, configurations of symmetric elastic plates under pressure, Hopf Bifurcation, Taylor vortices, convective motions of fluids, oscillations of chemical reactions, etc . . . Some of these problems have been tackled recently by different techniques using equivariant versions of Degree, Singularity and Variations. The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in Nonlinear Analysis during the last two-three decades. The survey articles presented here reflect the personal taste and points of view of the authors (all of them well-known and distinguished specialists in their own fields) on the subject matter. A common feature of these papers is that of start ing with an historical introductory background of the different disciplines under consideration and climbing up to the heights of the most recent re sults.

Integrable Systems in the realm of Algebraic Geometry

2013-11-11 Mathematics
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Release : 2013-11-11
Genre : Mathematics
Kind : eBook
Book Rating : 357/5 ( reviews)

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Book Synopsis Integrable Systems in the realm of Algebraic Geometry by : Pol Vanhaecke

Download or read book Integrable Systems in the realm of Algebraic Geometry written by Pol Vanhaecke. This book was released on 2013-11-11. Available in PDF, EPUB and Kindle. Book excerpt: Integrable systems are related to algebraic geometry in many different ways. This book deals with some aspects of this relation, the main focus being on the algebraic geometry of the level manifolds of integrable systems and the construction of integrable systems, starting from algebraic geometric data. For a rigorous account of these matters, integrable systems are defined on affine algebraic varieties rather than on smooth manifolds. The exposition is self-contained and is accessible at the graduate level; in particular, prior knowledge of integrable systems is not assumed.

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