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## Details

Document Type: | Book |
---|---|

All Authors / Contributors: |
James D Louck; M L Stein |

ISBN: | 9789814632416 9814632414 |

OCLC Number: | 894032954 |

Description: | xii, 179 pages : illustrations ; 26 cm |

Contents: | Introduction and point of view -- Recursive construction -- Description of events in the inverse graph -- The (1+1)-dimensional nonlinear universe -- The creation table -- Graphical presentation of MSS roots -- Graphical presentation of inverse graphs. |

Other Titles: | Nonlinear universe of the parabolic map and combinatorics |

Responsibility: | James D. Louck, Myron L. Stein. |

### Abstract:

"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"--The publisher.

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