Screen LibraryThe (1+1)-nonlinear universe of the parabolic map and combinatorics /
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 parab...
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| Main Authors: | |
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| Group Author: | |
| Published: |
World Scientific Publishing Co. Pte. Ltd.,
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| Publisher Address: | Singapore ; Hackensack, NJ : |
| Publication Dates: | [2015] |
| Literature type: | Book |
| Language: | English |
| Subjects: | |
| 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 th |
| Carrier Form: | xii, 179 pages : illustrations ; 26 cm |
| Bibliography: | Includes bibliographical references (page 171-174) and index. |
| ISBN: |
9789814632416 (hardcover) : 9814632414 (hardcover) |
| Index Number: | QA427 |
| CLC: | O157.1 |
| Call Number: | O157.1/L886-1 |
| Contents: | 1. Introduction and point of view. 1.1. Function composition and graphs. 1.2. Inverse graphs created at [symbol] = 1. 1.3. Preview of the full [symbol]-evolution. 1.4. The baseline. 1.5. Vocabulary, symbol definitions, and explanations -- 2. Recursive construction. 2.1. Construction of the baseline B[symbol]. 2.2. Reducible and irreducible sequences -- 3. Description of events in the inverse graph. 3.1. Domains of definition of branches and curves. 3.2. Concatenation, harmonics, and antiharmonics. 3.3. Fixed points as dynamical objects. 3.4. The fabric of bifurcation events. 3.5. The anatomy |