The (1+1)-Nonlinear Universe of the Parabolic Map and Combinatorics

Nonfiction, Science & Nature, Mathematics, Combinatorics, Science, Physics, Chaotic Behavior
Cover of the book The (1+1)-Nonlinear Universe of the Parabolic Map and Combinatorics by James D Louck, Myron L Stein*, World Scientific Publishing Company
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: James D Louck, Myron L Stein* ISBN: 9789814632430
Publisher: World Scientific Publishing Company Publication: December 30, 2014
Imprint: WSPC Language: English
Author: James D Louck, Myron L Stein*
ISBN: 9789814632430
Publisher: World Scientific Publishing Company
Publication: December 30, 2014
Imprint: WSPC
Language: English

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

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

Readership: Post-graduates from mathematics and physics backgrounds, mathematics and physics professionals with an interest in astrophysics.
Key Features:

  • There exists a unique inverse graph. This unique graph can be constructed from a simple algorithm
  • The concept of a deterministic inverse graph and its relationship to complex adaptive systems is new
  • This monograph is of general value to readers because it illustrates nicely that research in new methodologies in Mathematics can lead to new insights in Physics
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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

Contents:

Readership: Post-graduates from mathematics and physics backgrounds, mathematics and physics professionals with an interest in astrophysics.
Key Features:

More books from World Scientific Publishing Company

Cover of the book Lectures on Quantum Computing, Thermodynamics and Statistical Physics by James D Louck, Myron L Stein*
Cover of the book Uncertainty Modelling in Knowledge Engineering and Decision Making by James D Louck, Myron L Stein*
Cover of the book Silicon Solid State Devices and Radiation Detection by James D Louck, Myron L Stein*
Cover of the book Mechanics of Elastic Solids by James D Louck, Myron L Stein*
Cover of the book Hypernetworks in the Science of Complex Systems by James D Louck, Myron L Stein*
Cover of the book Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras by James D Louck, Myron L Stein*
Cover of the book Flexoelectricity in Solids by James D Louck, Myron L Stein*
Cover of the book 50 Years of Social Issues in Singapore by James D Louck, Myron L Stein*
Cover of the book Newton and the Great World System by James D Louck, Myron L Stein*
Cover of the book The Young Scientists Series by James D Louck, Myron L Stein*
Cover of the book Social Structure of Contemporary China by James D Louck, Myron L Stein*
Cover of the book Photosynthesis by James D Louck, Myron L Stein*
Cover of the book Biology and Pathogenesis of Rhabdo- and Filoviruses by James D Louck, Myron L Stein*
Cover of the book Genetic Privacy by James D Louck, Myron L Stein*
Cover of the book Dark Matter, Neutrinos, and Our Solar System by James D Louck, Myron L Stein*
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy