The Plaid Model : : (AMS-198) / / Richard Evan Schwartz.

• Superior document: Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English
• VerfasserIn: Schwartz, Richard Evan,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2019]; ©2019
• Year of Publication: 2019
• Language: English
• Series: Annals of Mathematics Studies ; 198
• Physical Description: 1 online resource (280 p.)

Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. The Plaid Model, which is a self-contained sequel to Richard Schwartz's Outer Billiards on Kites, provides a combinatorial model for orbits of outer billiards on kites.Schwartz relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called "the plaid model," has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics.The book includes an extensive computer program that allows readers to explore materials interactively and each theorem is accompanied by a computer demo.

Table of Contents

Frontmatter -- Contents -- Preface -- Introduction -- Part 1. The Plaid Model -- Chapter 1. Definition of the Plaid Model -- Chapter 2. Properties of the Model -- Chapter 3. Using the Model -- Chapter 4. Particles and Spacetime Diagrams -- Chapter 5. Three-Dimensional Interpretation -- Chapter 6. Pixellation and Curve Turning -- Chapter 7. Connection to the Truchet Tile System -- Part 2. The Plaid PET -- Chapter 8. The Plaid Master Picture Theorem -- Chapter 9. The Segment Lemma -- Chapter 10. The Vertical Lemma -- Chapter 11. The Horizontal Lemma -- Chapter 12. Proof of the Main Result -- Part 3. The Graph PET -- Chapter 13. Graph Master Picture Theorem -- Chapter 14. Pinwheels and Quarter Turns -- Chapter 15. Quarter Turn Compositions and PETs -- Chapter 16. The Nature of the Compactification -- Part 4. The Plaid-Graph Correspondence -- Chapter 17. The Orbit Equivalence Theorem -- Chapter 18. The Quasi-Isomorphism Theorem -- Chapter 19. Geometry of the Graph Grid -- Chapter 20. The Intertwining Lemma -- Part 5. The Distribution of Orbits -- Chapter 21. Existence of Infinite Orbits -- Chapter 22. Existence of Many Large Orbits -- Chapter 23. Infinite Orbits Revisited -- Chapter 24. Some Elementary Number Theory -- Chapter 25. The Weak and Strong Case -- Chapter 26. The Core Case -- References -- Index