The 1 1 nonlinear Universe Of The Parabolic Map And Combinatorics is popular PDF and ePub book, written by James D Louck in 2014-12-30, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The 1 1 nonlinear Universe Of The Parabolic Map And Combinatorics can be Read Online from any device for your convenience.
The 1 1 nonlinear Universe Of The Parabolic Map And Combinatorics Book PDF Summary
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
Detail Book of The 1 1 nonlinear Universe Of The Parabolic Map And Combinatorics PDF
- Author : James D Louck
- Release : 30 December 2014
- Publisher : World Scientific
- ISBN : 9789814632430
- Genre : Mathematics
- Total Page : 192 pages
- Language : English
- PDF File Size : 15,9 Mb
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