{"product_id":"9789814632430","title":"The (1+ 1)-nonlinear Universe Of The Parabolic Map And Combinatorics","description":"\u003cp\u003eThis 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 \u003ci\u003ex\u003c\/i\u003e = 1 may be viewed as a time-like parameter, which together with the \u003ci\u003ex\u003c\/i\u003e-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 \u003ci\u003en\u003c\/i\u003e-fold composition of the basic parabola with itself. However, it is the properties of the graph inverse to this \u003ci\u003en\u003c\/i\u003e-fold composition that are the objects whose properties are developed. The reflection symmetry of the basic parabola through the vertical line \u003ci\u003ex\u003c\/i\u003e = 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 \u003ci\u003ex\u003c\/i\u003e-coordinate, the entire theory, of course, being highly nonlinear — it is polynomial in the time-like parameter and in the \u003ci\u003ex\u003c\/i\u003e-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.\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e\u003cp\u003e* \u003ci\u003edeceased\u003c\/i\u003e\u003c\/p\u003e\u003cb\u003eContents:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eIntroduction and Point of View\u003c\/li\u003e\n\u003cli\u003eRecursive Construction\u003c\/li\u003e\n\u003cli\u003eDescription of Events in the Inverse Graph\u003c\/li\u003e\n\u003cli\u003eThe (1+1)-Dimensional Nonlinear Universe\u003c\/li\u003e\n\u003cli\u003eThe Creation Table\u003c\/li\u003e\n\u003cli\u003eGraphical Presentation of MSS Roots\u003c\/li\u003e\n\u003cli\u003eGraphical Presentation of Inverse Graphs\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cb\u003eReadership:\u003c\/b\u003e Post-graduates from mathematics and physics backgrounds, mathematics and physics professionals with an interest in astrophysics.\u003cbr\u003e\u003cb\u003eKey Features:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eThere exists a unique inverse graph. This unique graph can be constructed from a simple algorithm\u003c\/li\u003e\n\u003cli\u003eThe concept of a deterministic inverse graph and its relationship to complex adaptive systems is new\u003c\/li\u003e\n\u003cli\u003eThis monograph is of general value to readers because it illustrates nicely that research in new methodologies in Mathematics can lead to new insights in Physics\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47185305239792,"sku":"9789814632430","price":35.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814632430_p0.jpg?v=1763692139","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814632430","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}