Analytic Theory of Global Bifurcation
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A01=Boris Buffoni
A01=John Toland
Algebraic equation
Analytic function
Analytic manifold
Author_Boris Buffoni
Author_John Toland
Banach space
Bifurcation diagram
Bifurcation theory
Boundary value problem
Bounded operator
Bounded set (topological vector space)
Cartesian coordinate system
Category=PBKJ
Category=PBPH
Codimension
Complex analysis
Complex conjugate
Complex number
Connected space
Coordinate system
Derivative
Diagram (category theory)
Differentiable function
Differentiable manifold
Dimension
Dimension (vector space)
Eigenvalues and eigenvectors
Elliptic integral
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Euler equations (fluid dynamics)
Existential quantification
Fredholm operator
Froude number
Functional analysis
Hilbert space
Homeomorphism
Implicit function theorem
Linear algebra
Linear function
Linear independence
Linear map
Linear space (geometry)
Linear subspace
Linearity
Linearization
Metric space
Morse theory
Multilinear form
Open mapping theorem (complex analysis)
Operator (physics)
Ordinary differential equation
Parametrization
Partial differential equation
Permutation
Permutation group
Polynomial
Power series
Prime number
Proportionality (mathematics)
Pseudo-differential operator
Puiseux series
Resultant
Singularity theory
Skew-symmetric matrix
Solution set
Special case
Sturm-Liouville theory
Symmetric bilinear form
Taylor series
Taylor's theorem
Theorem
Union (set theory)
Variable (mathematics)
Vector space
Product details
- ISBN 9780691112985
- Weight: 397g
- Dimensions: 152 x 235mm
- Publication Date: 02 Feb 2003
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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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.
Boris Buffoni holds a Swiss National Science Foundation Professorship in Mathematics at the Swiss Federal Institute of Technology-Lausanne. John Toland is Professor of Mathematical Sciences at the University of Bath and a Senior Research Fellow of the UK's Engineering and Physical Sciences Research Council
