{"product_id":"complex-dynamics-and-renormalization-am-135-curtis-t-mcmullen-9780691029818","title":"Complex Dynamics and Renormalization (Am-135), Volume 135","description":"\u003cp\u003eAddressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an \u003ci\u003einfinitely renormalizable\u003c\/i\u003e quadratic polynomial \u003ci\u003ef(z) = z2 + c\u003c\/i\u003e. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial \u003ci\u003ef\u003c\/i\u003e. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Curtis T. McMullen\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0691029814\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780691029818\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 12\/19\/1994\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 214\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.60lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.22h x 6.12w x 0.61d","brand":"Curtis T. McMullen","offers":[{"title":"Paperback","offer_id":44449929887999,"sku":"9780691029818","price":84.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_740a2692-fad9-40c9-876d-7237081ce953.jpg?v=1698501806","url":"https:\/\/www.whiterainbookhouse.com\/products\/complex-dynamics-and-renormalization-am-135-curtis-t-mcmullen-9780691029818","provider":"WR Book House","version":"1.0","type":"link"}