Octogonal PETs / Richard Evan Schwartz.
Material type:
TextSeries: Mathematical surveys and monographs ; v 197Publication details: Providence : American Mathematical Society, c2014.Description: x, 212 p. : illustrations (some color) ; 26 cmISBN: - 9781470415228 (alk. paper)
- Octogonal polytope exchange transformations
- 510MS 23 Am512
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 510MS Am512 (Browse shelf(Opens below)) | Available | 135870 |
Browsing ISI Library, Kolkata shelves Close shelf browser (Hides shelf browser)
| 510MS Am512 Stochastic resonance : | 510MS Am512 Complex multiplication and lifting problems / | 510MS Am512 Geometry of isotropic convex bodies / | 510MS Am512 Octogonal PETs / | 510MS Am512 Brauer groups, tamagawa measures, and rational points on algebraic varieties / | 510MS Am512 Foundations of free noncommutative function theory / | 510MS Am512 Nonlinear elliptic equations and nonassociative algebras / |
Includes bibliographical references.
1. Introduction --
2. Background --
3. Multigraph PETs --
4. The alternating grid system --
5. Outer billiards on semiregular octagons --
6. Quarter turn compositions --
7. Elementary properties --
8. Orbit stability and combinatorics --
9. Bilateral symmetry --
10. Proof of the main theorem --
11. The renormalization map --
12. Properties of the tiling --
13. The filling lemma --
14. The covering lemma --
15. Further geometric results --
16. Properties of the limit set --
17. Hausdorff convergence --
18. Recurrence relations --
19. Hausdorff dimension bounds --
20. Controlling the limit set --
21. The arc case - - 22. Further symmetries of the tiling --
23. The forest case --
24. The cantor set case --
25. Dynamics in the arc case --
26. Computational methods --
27. The calculations --
28. The raw data--
Bibliography.
This book introduces a general method for constructing polytope exchange transformations in higher dimensions and then studies the simplest example of the construction in detail. The simplest case is a 1-parameter family of polygon exchange transformations that turns out to be closely related to outer billiards on semi-regular octagons. The 1-parameter family admits a complete renormalization scheme, and this structure allows for a fairly complete analysis both of the system and of outer billiards on semi-regular octagons. The material in this book was discovered through computer experimentation. On the other hand, the proofs are traditional, except for a few rigorous computer-assisted calculations.
There are no comments on this title.
