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Könyv Analytic Theory of Global Bifurcation John Toland

Analytic Theory of Global Bifurcation

Szerző: John Toland, Boris Buffoni
Nyelv: Angol
Kötés: Kemény kötésű
Kiadó: Princeton University Press
Elérhetőség: Beszállítói készleten
Küldés 14-21 napon belül
42 905 Ft
Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter...

Információk a könyvről

Szerző
John Toland, Boris Buffoni
Nyelv
Angol
Kötés
Könyv - Kemény kötésű
Kiadva
2003
oldal
184
EAN
9780691112985
ISBN
0691112983
Enbook ID
05145314
Kiadó
Princeton University Press
Súly
397
Méretek
152 x 235 x 14

Teljes leírás

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.

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