{"product_id":"the-1-1-nonlinear-universe-of-james-d-louck-9789814632416","title":"The (1+ 1)-Nonlinear Universe of the Parabolic Map and Combinatorics","description":"This monograph develops chaos theory from properties of the graphs inverse to the parabolic map of the interval [0, 2], where the height at the midpoint x = 1 may be viewed as a time-like parameter, which together with the x-coordinate, provide the two parameters that uniquely characterize the parabola, and which are used throughout the monograph. There is only one basic mathematical operation used: function composition. The functions studied are the n-fold composition of the basic parabola with itself. However, it is the properties of the graph inverse to this n-fold composition that are the objects whose properties are developed. The reflection symmetry of the basic parabola through the vertical line x = 1 gives rise to two symmetry classes of inverse graphs: the inverse graphs and their conjugates. Quite remarkably, it turns out that there exists, among all the inverse graphs and their conjugates, a completely deterministic class of inverse graphs and their conjugates. Deterministic in the sense that this class is uniquely determined for all values of the time-like parameter and the x-coordinate, the entire theory, of course, being highly nonlinear -- it is polynomial in the time-like parameter and in the x-coordinate. The deterministic property and its implementation are key to the argument that the system is a complex adaptive system in the sense that a few axioms lead to structures of unexpected richness.This monograph is about working out the many details that advance the notion that deterministic chaos theory, as realized by a complex adaptive system, is indeed a new body of mathematics that enriches our understanding of the world around us. But now the imagination is also opened to the possibility that the real universe is a complex adaptive system.* deceased\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e James D. Louck, Myron L. Stein\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 9814632414\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9789814632416\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e World Scientific Publishing Company\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 03\/04\/2015\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 192\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.20lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.80h x 6.50w x 0.80d","brand":"James D. Louck","offers":[{"title":"Hardcover","offer_id":44126133518591,"sku":"9789814632416","price":88.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_43a9af0c-944a-464a-8158-a2c44466f3fd.jpg?v=1687446458","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-1-1-nonlinear-universe-of-james-d-louck-9789814632416","provider":"WR Book House","version":"1.0","type":"link"}