{"product_id":"analytic-theory-of-global-bifurcation-boris-buffoni-9780691112985","title":"Analytic Theory of Global Bifurcation","description":"\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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Boris Buffoni, John Toland\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0691112983\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780691112985\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Princeton University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 02\/02\/2003\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 184\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.90lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.72h x 6.56w x 0.76d","brand":"Boris Buffoni","offers":[{"title":"Hardcover","offer_id":44120039751935,"sku":"9780691112985","price":90.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_99b9336a-b229-4a2b-ad1e-99eab60a92cc.jpg?v=1687412242","url":"https:\/\/www.whiterainbookhouse.com\/products\/analytic-theory-of-global-bifurcation-boris-buffoni-9780691112985","provider":"WR Book House","version":"1.0","type":"link"}