The 1+1-nonlinear Universe of the Parabolic Map and Combinatorics - Rilegato

Rilegato

ISBN 10: 9814632414 ISBN 13: 9789814632416

Casa editrice: World Scientific Pub Co Inc, 2015

Riassunto

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 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.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.

Dettagli dell'edizione

• Editore: World Scientific Pub Co Inc
• Data di pubblicazione: 2015
• Lingua: Inglese
• ISBN 10: 9814632414
• ISBN 13: 9789814632416
• Rilegatura: Copertina rigida
• Numero di pagine: 179
• Redattore: Louck James D., Stein Myron L.
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile