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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

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Table of Contents

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Front/Back Matter

• View this volume's front and 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