Octogonal PETs /

510MS
Am512

135870

Schwartz, Richard Evan. Octogonal PETs / Richard Evan Schwartz. - Providence : American Mathematical Society, c2014.
x, 212 p. : illustrations (some color) ; 26 cm. - (Mathematical surveys and monographs ; v 197) Content notes : 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. 9781470415228 (alk. paper) * Polytopes. Geometry. Dynamical systems and ergodic theory -- Low-dimensional dynamical systems -- Universality, renormalization. * Series