Analytic Theory of Global Bifurcation : An Introduction /
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...
Clasificación: | Libro Electrónico |
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Autores principales: | , |
Formato: | Electrónico eBook |
Idioma: | Inglés |
Publicado: |
Princeton, NJ :
Princeton University Press,
[2016]
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Colección: | Princeton Series in Applied Mathematics ;
55 |
Temas: | |
Acceso en línea: | Texto completo Texto completo |
MARC
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100 | 1 | |a Buffoni, Boris, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Analytic Theory of Global Bifurcation : |b An Introduction / |c John Toland, Boris Buffoni. |
264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2016] | |
264 | 4 | |c ©2003 | |
300 | |a 1 online resource (184 p.) : |b 5 line illus. | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a Princeton Series in Applied Mathematics ; |v 55 | |
505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t Chapter 1. Introduction -- |t Part 1. Linear and Nonlinear Functional Analysis -- |t Chapter 2. Linear Functional Analysis -- |t Chapter 3. Calculus in Banach Spaces -- |t Chapter 4. Multilinear and Analytic Operators -- |t Part 2. Analytic Varieties -- |t Chapter 5. Analytic Functions on Fn -- |t Chapter 6. Polynomials -- |t Chapter 7. Analytic Varieties -- |t Part 3. Bifurcation Theory -- |t Chapter 8. Local Bifurcation Theory -- |t Chapter 9. Global Bifurcation Theory -- |t Part IV. Stokes Waves -- |t Chapter 10. Steady Periodic Water Waves -- |t Chapter 11. Global Existence of Stokes Waves -- |t Bibliography -- |t Index |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a 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. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
650 | 0 | |a Bifurcation theory. | |
650 | 7 | |a MATHEMATICS / Applied. |2 bisacsh | |
653 | |a Addition. | ||
653 | |a Algebraic equation. | ||
653 | |a Analytic function. | ||
653 | |a Analytic manifold. | ||
653 | |a Atmospheric pressure. | ||
653 | |a Banach space. | ||
653 | |a Bernhard Riemann. | ||
653 | |a Bifurcation diagram. | ||
653 | |a Bifurcation theory. | ||
653 | |a Boundary value problem. | ||
653 | |a Bounded operator. | ||
653 | |a Bounded set (topological vector space). | ||
653 | |a Boundedness. | ||
653 | |a Canonical form. | ||
653 | |a Cartesian coordinate system. | ||
653 | |a Codimension. | ||
653 | |a Compact operator. | ||
653 | |a Complex analysis. | ||
653 | |a Complex conjugate. | ||
653 | |a Complex number. | ||
653 | |a Connected space. | ||
653 | |a Coordinate system. | ||
653 | |a Corollary. | ||
653 | |a Curvature. | ||
653 | |a Derivative. | ||
653 | |a Diagram (category theory). | ||
653 | |a Differentiable function. | ||
653 | |a Differentiable manifold. | ||
653 | |a Dimension (vector space). | ||
653 | |a Dimension. | ||
653 | |a Direct sum. | ||
653 | |a Eigenvalues and eigenvectors. | ||
653 | |a Elliptic integral. | ||
653 | |a Embedding. | ||
653 | |a Equation. | ||
653 | |a Euclidean division. | ||
653 | |a Euler equations (fluid dynamics). | ||
653 | |a Existential quantification. | ||
653 | |a First principle. | ||
653 | |a Fredholm operator. | ||
653 | |a Froude number. | ||
653 | |a Functional analysis. | ||
653 | |a Hilbert space. | ||
653 | |a Homeomorphism. | ||
653 | |a Implicit function theorem. | ||
653 | |a Integer. | ||
653 | |a Linear algebra. | ||
653 | |a Linear function. | ||
653 | |a Linear independence. | ||
653 | |a Linear map. | ||
653 | |a Linear programming. | ||
653 | |a Linear space (geometry). | ||
653 | |a Linear subspace. | ||
653 | |a Linearity. | ||
653 | |a Linearization. | ||
653 | |a Metric space. | ||
653 | |a Morse theory. | ||
653 | |a Multilinear form. | ||
653 | |a N0. | ||
653 | |a Natural number. | ||
653 | |a Neumann series. | ||
653 | |a Nonlinear functional analysis. | ||
653 | |a Nonlinear system. | ||
653 | |a Numerical analysis. | ||
653 | |a Open mapping theorem (complex analysis). | ||
653 | |a Operator (physics). | ||
653 | |a Ordinary differential equation. | ||
653 | |a Parameter. | ||
653 | |a Parametrization. | ||
653 | |a Partial differential equation. | ||
653 | |a Permutation group. | ||
653 | |a Permutation. | ||
653 | |a Polynomial. | ||
653 | |a Power series. | ||
653 | |a Prime number. | ||
653 | |a Proportionality (mathematics). | ||
653 | |a Pseudo-differential operator. | ||
653 | |a Puiseux series. | ||
653 | |a Quantity. | ||
653 | |a Real number. | ||
653 | |a Resultant. | ||
653 | |a Singularity theory. | ||
653 | |a Skew-symmetric matrix. | ||
653 | |a Smoothness. | ||
653 | |a Solution set. | ||
653 | |a Special case. | ||
653 | |a Standard basis. | ||
653 | |a Sturm-Liouville theory. | ||
653 | |a Subset. | ||
653 | |a Symmetric bilinear form. | ||
653 | |a Symmetric group. | ||
653 | |a Taylor series. | ||
653 | |a Taylor's theorem. | ||
653 | |a Theorem. | ||
653 | |a Total derivative. | ||
653 | |a Two-dimensional space. | ||
653 | |a Union (set theory). | ||
653 | |a Variable (mathematics). | ||
653 | |a Vector space. | ||
653 | |a Zero of a function. | ||
700 | 1 | |a Toland, John, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Series in Applied Mathematics eBook-Package |z 9783110515831 |o ZDB-23-PAM |
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