Analytic Theory of Global Bifurcation

An Introduction

Boris Buffoni, John Toland

170 pages, parution le 24/03/2003

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Résumé

Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of continuous parameter dependence of solutions by showing that there are connected sets of solutions of global extent. Even when the operators are infinitely differentiable in all the variables and parameters, connectedness here cannot in general be replaced by path-connectedness. However, in the context of real-analyticity there is an alternative theory of global bifurcation due to Dancer, which offers a much stronger notion of parameter dependence.
This book aims to develop from first principles Dancer's global bifurcation theory for one-parameter families of real-analytic operators in Banach spaces. It shows that there are globally defined continuous and locally real-analytic curves of solutions. In particular, in the real-analytic setting, local analysis can lead to global consequences--for example, as explained in detail here, those resulting from bifurcation from a simple eigenvalue. Included are accounts of analyticity and implicit function theorems in Banach spaces, classical results from the theory of finite-dimensional analytic varieties, and the links between these two and global existence theory.
Laying the foundations for more extensive studies of real-analyticity in infinite-dimensional problems and illustrating the theory with examples, Analytic Theory of Global Bifurcation is intended for graduate students and researchers in pure and applied analysis.

Contents

Chapter 1. Introduction

PART 1. LINEAR AND NONLINEAR FUNCTIONAL ANALYSIS

Chapter 2. Linear functional analysis
Chapter 3. Calculus in Banach Spaces
Chapter 4. Multilinear and Analytic Operators

PART 2. ANALYTIC VARIETIES

Chapter 5. Analytic Functions on Fⁿ
Chapter 6. Polynomials
Chapter 7. Analytic Varieties

PART 3. BIFURCATION THEORY

Chapter 8. Local Bifurcation Theory
Chapter 9. Global Bifurcation Theory

PART 4. STOKES WAVES

Chapter 10. Steady Periodic Water Waves
Chapter 11. Global Existence

L'auteur - John Toland

Outre sa biographie d'Hitler, John Toland (1912-2004) a publié plusieurs livres sur la Seconde Guerre Mondiale qui sont autant de classiques, en particulier Les 100 derniers jours : 27 janvier-8 mai 1945 et L'Empire du Soleil-Levant : gloire et chute, 1936-1945 qui a reçu le prix Pulitzer.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Princeton University Press
Auteur(s)	Boris Buffoni, John Toland
Parution	24/03/2003
Nb. de pages	170
Format	16 x 24
Couverture	Relié
Poids	405g
Intérieur	Noir et Blanc
EAN13	9780691112985
ISBN13	978-0-691-11298-5