{"product_id":"analytic-theory-of-global-bifurcation-hardcover","title":"Analytic Theory of Global Bifurcation - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eBoris Buffoni\u003c\/b\u003e (Author), \u003cb\u003eJohn Toland\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eRabinowitz'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. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e 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. \u003cp\u003e\u003c\/p\u003e Laying the foundations for more extensive studies of real-analyticity in infinite-dimensional problems and illustrating the theory with examples, \u003ci\u003e Analytic Theory of Global Bifurcation\u003c\/i\u003e is intended for graduate students and researchers in pure and applied analysis.\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cb\u003eBoris Buffoni\u003c\/b\u003e holds a Swiss National Science Foundation Professorship in Mathematics at the Swiss Federal Institute of Technology-Lausanne. \u003cb\u003eJohn Toland\u003c\/b\u003e 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\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 184\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.76 x 9.72 x 6.56 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e February 02, 2003\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":52704553828659,"sku":"9780691112985","price":176.29,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0300\/5595\/6612\/files\/WlIxS2I4TkJlL1psR2UvQVprQytQZz09.webp?v=1763359095","url":"https:\/\/www.vysn.com\/products\/analytic-theory-of-global-bifurcation-hardcover","provider":"VYSN","version":"1.0","type":"link"}