Outer Billiards on Kites (AM-171) / / Richard Evan Schwartz.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Schwartz, Richard Evan,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2009]; ©2010
• Year of Publication: 2009
• Edition: Course Book
• Language: English
• Series: Annals of Mathematics Studies ; 171
• Physical Description: 1 online resource (320 p.) :; 64 halftones. 35 line illus.

Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B. H. Neumann introduced this system in the 1950s, and J. Moser popularized it as a toy model for celestial mechanics. All along, the so-called Moser-Neumann question has been one of the central problems in...

Table of Contents

• Frontmatter
• Contents
• Preface
• Chapter 1. Introduction
• Part 1. The Erratic Orbits Theorem
• Chapter 2. The Arithmetic Graph
• Chapter 3. The Hexagrid Theorem
• Chapter 4. Period Copying
• Chapter 5. Proof of the Erratic Orbits Theorem
• Part 2. The Master Picture Theorem
• Chapter 6. The Master Picture Theorem
• Chapter 7. The Pinwheel Lemma
• Chapter 8. The Torus Lemma
• Chapter 9. The Strip Functions
• Chapter 10. Proof of the Master Picture Theorem
• Part 3. Arithmetic Graph Structure Theorems
• Chapter 11. Proof of the Embedding Theorem
• Chapter 12. Extension and Symmetry
• Chapter 13. Proof of Hexagrid Theorem I
• Chapter 14. The Barrier Theorem
• Chapter 15. Proof of Hexagrid Theorem II
• Chapter 16. Proof of the Intersection Lemma
• Part 4. Period-Copying Theorems
• Chapter 17. Diophantine Approximation
• Chapter 18. The Diophantine Lemma
• Chapter 19. The Decomposition Theorem
• Chapter 20. Existence of Strong Sequences
• Part 5. The Comet Theorem
• Chapter 21. Structure of the Inferior and Superior Sequences
• Chapter 22. The Fundamental Orbit
• Chapter 23. The Comet Theorem
• Chapter 24. Dynamical Consequences
• Chapter 25. Geometric Consequences
• Part 6. More Structure Theorems
• Chapter 26. Proof of the Copy Theorem
• Chapter 27. Pivot Arcs in the Even Case
• Chapter 28. Proof of the Pivot Theorem
• Chapter 29. Proof of the Period Theorem
• Chapter 30. Hovering Components
• Chapter 31. Proof of the Low Vertex Theorem
• Appendix
• Bibliography
• Index