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The Octagonal PETs
About this Title
Richard Evan Schwartz, Brown University, Providence, RI
Publication: Mathematical Surveys and Monographs
Publication Year:
2014; Volume 197
ISBNs: 978-1-4704-1522-8 (print); 978-1-4704-1718-5 (online)
DOI: https://doi.org/10.1090/surv/197
MathSciNet review: MR3186232
MSC: Primary 37E20; Secondary 37E05, 37E15
Table of Contents
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Front/Back Matter
Chapters
- Chapter 1. Introduction
Part 1. Friends of the octagonal PETs
- Chapter 2. Background
- Chapter 3. Multigraph PETs
- Chapter 4. The alternating grid system
- Chapter 5. Outer billiards on semiregular octagons
- Chapter 6. Quarter turn compositions
Part 2. Renormalization and symmetry
- Chapter 7. Elementary properties
- Chapter 8. Orbit stability and combinatorics
- Chapter 9. Bilateral symmetry
- Chapter 10. Proof of the main theorem
- Chapter 11. The renormalization map
- Chapter 12. Properties of the tiling
Part 3. Metric properties
- Chapter 13. The filling lemma
- Chapter 14. The covering lemma
- Chapter 15. Further geometric results
- Chapter 16. Properties of the limit set
- Chapter 17. Hausdorff convergence
- Chapter 18. Recurrence relations
- Chapter 19. Hausdorff dimension bounds
Part 4. Topological properties
- Chapter 20. Controlling the limit set
- Chapter 21. The arc case
- Chapter 22. Further symmetries of the tiling
- Chapter 23. The forest case
- Chapter 24. The Cantor set case
- Chapter 25. Dynamics in the arc case
Part 5. Computational details
- Chapter 26. Computational methods
- Chapter 27. The calculations
- Chapter 28. The raw data