{"product_id":"the-1-1-nonlinear-universe-of-the-parabolic-map-and-combinatorics-hardcover","title":"The (1+ 1)-Nonlinear Universe of the Parabolic Map and Combinatorics - Hardcover","description":"\u003cp\u003eby \u003cb\u003eJames D. Louck\u003c\/b\u003e (Author), \u003cb\u003eMyron L. Stein\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\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 \u003cem\u003ex\u003c\/em\u003e = 1 may be viewed as a time-like parameter, which together with the \u003cem\u003ex\u003c\/em\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 \u003cem\u003en\u003c\/em\u003e-fold composition of the basic parabola with itself. However, it is the properties of the graph inverse to this \u003cem\u003en\u003c\/em\u003e-fold composition that are the objects whose properties are developed. The reflection symmetry of the basic parabola through the vertical line \u003cem\u003ex\u003c\/em\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 \u003cem\u003ex\u003c\/em\u003e-coordinate, the entire theory, of course, being highly nonlinear -- it is polynomial in the time-like parameter and in the \u003cem\u003ex\u003c\/em\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\u003ch3\u003eFront Jacket\u003c\/h3\u003e\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 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 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 keys 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\u003e 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.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 192\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.8 x 9.8 x 6.5 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e March 04, 2015\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42729877930047,"sku":"9789814632416","price":171.07,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/9650914490c1cbd63c704eda8adb3694.webp?v=1765123946","url":"https:\/\/dhlswag.com\/products\/the-1-1-nonlinear-universe-of-the-parabolic-map-and-combinatorics-hardcover","provider":"BBB","version":"1.0","type":"link"}