Chapters in this book

1. Frontmatter i
2. Contents v
3. Preface xi
4. Chapter 1. Introduction 1
5. Part 1. The Erratic Orbits Theorem
6. Chapter 2. The Arithmetic Graph 19
7. Chapter 3. The Hexagrid Theorem 33
8. Chapter 4. Period Copying 41
9. Chapter 5. Proof of the Erratic Orbits Theorem 45
10. Part 2. The Master Picture Theorem
11. Chapter 6. The Master Picture Theorem 55
12. Chapter 7. The Pinwheel Lemma 69
13. Chapter 8. The Torus Lemma 77
14. Chapter 9. The Strip Functions 85
15. Chapter 10. Proof of the Master Picture Theorem 93
16. Part 3. Arithmetic Graph Structure Theorems
17. Chapter 11. Proof of the Embedding Theorem 101
18. Chapter 12. Extension and Symmetry 107
19. Chapter 13. Proof of Hexagrid Theorem I 117
20. Chapter 14. The Barrier Theorem 125
21. Chapter 15. Proof of Hexagrid Theorem II 133
22. Chapter 16. Proof of the Intersection Lemma 143
23. Part 4. Period-Copying Theorems
24. Chapter 17. Diophantine Approximation 153
25. Chapter 18. The Diophantine Lemma 163
26. Chapter 19. The Decomposition Theorem 171
27. Chapter 20. Existence of Strong Sequences 181
28. Part 5. The Comet Theorem
29. Chapter 21. Structure of the Inferior and Superior Sequences 187
30. Chapter 22. The Fundamental Orbit 193
31. Chapter 23. The Comet Theorem 205
32. Chapter 24. Dynamical Consequences 219
33. Chapter 25. Geometric Consequences 227
34. Part 6. More Structure Theorems
35. Chapter 26. Proof of the Copy Theorem 239
36. Chapter 27. Pivot Arcs in the Even Case 249
37. Chapter 28. Proof of the Pivot Theorem 259
38. Chapter 29. Proof of the Period Theorem 273
39. Chapter 30. Hovering Components 279
40. Chapter 31. Proof of the Low Vertex Theorem 287
41. Appendix 295
42. Bibliography 303
43. Index 305