| 000 | 02558cam a22002898i 4500 | ||
|---|---|---|---|
| 001 | 135870 | ||
| 003 | ISI Library, Kolkata | ||
| 005 | 20150616115127.0 | ||
| 008 | 140225s2014 riu b 000 0 eng | ||
| 010 | _a 2014006823 | ||
| 020 | _a9781470415228 (alk. paper) | ||
| 040 | _aISI Library | ||
| 082 |
_a510MS _223 _bAm512 |
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| 100 | 1 | _aSchwartz, Richard Evan. | |
| 245 | 1 | 4 |
_aOctogonal PETs / _cRichard Evan Schwartz. |
| 246 | 3 | _aOctogonal polytope exchange transformations | |
| 260 |
_aProvidence : _bAmerican Mathematical Society, _cc2014. |
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| 300 |
_ax, 212 p. : _billustrations (some color) ; _c26 cm. |
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| 490 | 0 |
_aMathematical surveys and monographs ; _vv 197 |
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| 504 | _aIncludes bibliographical references. | ||
| 505 | 0 | _a1. 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. | |
| 520 | _aThis 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. | ||
| 650 | 0 | _aPolytopes. | |
| 650 | 0 | _aGeometry. | |
| 650 | 7 | _aDynamical systems and ergodic theory -- Low-dimensional dynamical systems -- Universality, renormalization. | |
| 942 |
_2ddc _cBK |
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| 999 |
_c419031 _d419031 |
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