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 bill...

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