# Analytic Theory of Global Bifurcation: An Introduction (Princeton Series in Applied Mathematics) download ebook

## by **John Toland,Boris Buffoni**

Boris Buffoni holds a Swiss National Science Foundation Professorship in Mathematics at the Swiss Federal Institute of Technology-Lausanne.

Boris Buffoni holds a Swiss National Science Foundation Professorship in Mathematics at the Swiss Federal Institute of Technology-Lausanne.

Princeton Series in Applied Mathematics This book aims to develop from first principles Dancer's global bifurcation theory for one-parameter families of real-analytic operators in Banach spaces.

Princeton Series in Applied Mathematics. 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. This book aims to develop from first principles Dancer's global bifurcation theory for one-parameter families of real-analytic operators in Banach spaces. The Princeton Series in Applied Mathematics publishes high quality advanced texts and monographs in all areas of applied mathematics. Books include those of a theoretical and general nature as well as those dealing with the mathematics of specific applications areas and real-world situations

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Buffoni, . Toland, . Analytic Theory of Global Bifurcation. An introduction, Princeton Series in Applied Mathematics. Princeton University Press, Princeton (2003)Google Scholar. 5. Buffoni, . Dancer, . The regularity and local bifurcation of steady periodic water waves. Kielhöfer, . Bifurcation Theory an Introduction with Applications to Partial Differential Equations, vol. 156, 2nd edn. Applied Mathematical Sciences, Springer, New York (2012)Google Scholar. 33. Moser, . A sharp form of an inequality by . rudinger.

Analytic theory of global bifurcation : an introduction, Boris Buffoni . Princeton series in applied mathematics. Morgan Kaufmann series in computer graphics and geometric modeling.

Analytic theory of global bifurcation : an introduction, Boris Buffoni and John Toland. PUBLISHER: Princeton, . Princeton University Press, 2003. SERIES: Princeton series in applied mathematics. Call number: Tk 6678.

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Boris Buffoni, John Willard T. .by Boris Buffoni, John Willard Toland. Published January 13, 2003 by Princeton University Press.

Boris Buffoni, John Willard T.Analytic Theory of Global Bifurcation (Princeton Series in Applied Mat. Are you sure you want to remove Analytic Theory of Global Bifurcation (Princeton Series in Applied Mathematics) from your list? Analytic Theory of Global Bifurcation (Princeton Series in Applied Mathematics).

Buffoni . Toland . Burckel, R. An Introduction to Classical Complex Analysis. Vol. 1. Pure and Applied Mathematics, 82. Princeton University Press, Princeton, NJ (2003). Digital Object Identifier: doi:10. 1515/9781400884339 Zentralblatt MATH: 1021. Academic Press, New York–London, 1979. Surface waves on steady perfect-fluid flows with vorticity. 64, 975–1007 (2011).

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.