{"product_id":"bifurcation-theory-hardback-9781470477943","title":"Bifurcation Theory (Hardback) 9781470477943","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eBifurcation Theory\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eAle Jan Homburg (Author), Jurgen Knobloch (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781470477943\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 31 January 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e646 pages\u003cbr\u003e25.4 x 17.8 x 3.4 cm, 1.116 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis textbook provides a thorough overview of bifurcation theory. Assuming some familiarity with differential equations and dynamical systems, it is suitable for use on advanced undergraduate and graduate level and can, in particular, be used for a graduate course on bifurcation theory.  The book combines a solid theoretical basis with a detailed description of classical bifurcations. It is organized in chapters on local, nonlocal, and global bifurcations; a number of appendices develop the toolbox for the study of bifurcations. The discussed local bifurcations include saddle-node and Hopf bifurcations, as well as the more advanced Bogdanov-Takens and Neimark-Sacker bifurcations. The book also covers nonlocal bifurcations, discussing various homoclinic bifurcations, and it surveys global bifurcations and phenomena, such as intermittency and period-doubling cascades. The book develops a broad range of complementary techniques, both geometric and analytic, for studying bifurcations. Techniques include normal form methods, center manifold reductions, the Lyapunov-Schmidt construction, cross-coordinate constructions, Melnikov's method, and Lin's method.  Full proofs of the results are provided, also for the material in the appendices. This includes proofs of the stable manifold theorem, of the center manifold theorem, and of Lin's method for studying homoclinic bifurcations.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cul\u003e\n\u003cli\u003eIntroductory models\u003c\/li\u003e\n\u003cli\u003eFlows and invariant sets\u003c\/li\u003e\n\u003cli\u003eLocal bifurcations\u003c\/li\u003e\n\u003cli\u003eNonlocal bifurcations\u003c\/li\u003e\n\u003cli\u003eGlobal bifurcations\u003c\/li\u003e\n\u003cli\u003eElements of nonlinear analysis\u003c\/li\u003e\n\u003cli\u003eInvariant manifolds and normal forms\u003c\/li\u003e\n\u003cli\u003eLin'\u003cbr\u003es method\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003c\/ul\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003c\/font\u003e","brand":"American Mathematical Society","offers":[{"title":"Brand New","offer_id":52589078675736,"sku":"9781470477943","price":92.69,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/freshlyprintedbooks.co.uk\/products\/bifurcation-theory-hardback-9781470477943","provider":"Freshly Printed Books","version":"1.0","type":"link"}