MARC details
| 000 -LEADER |
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| fixed length control field |
02558cam a22002898i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
135870 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
ISI Library, Kolkata |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20150616115127.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
140225s2014 riu b 000 0 eng |
| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER |
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| LC control number |
2014006823 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781470415228 (alk. paper) |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
ISI Library |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
510MS |
| Edition number |
23 |
| Item number |
Am512 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Schwartz, Richard Evan. |
| 245 14 - TITLE STATEMENT |
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| Title |
Octogonal PETs / |
| Statement of responsibility, etc |
Richard Evan Schwartz. |
| 246 3# - VARYING FORM OF TITLE |
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| Title proper/short title |
Octogonal polytope exchange transformations |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Providence : |
| Name of publisher, distributor, etc |
American Mathematical Society, |
| Date of publication, distribution, etc |
c2014. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
x, 212 p. : |
| Other physical details |
illustrations (some color) ; |
| Dimensions |
26 cm. |
| 490 0# - SERIES STATEMENT |
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| Series statement |
Mathematical surveys and monographs ; |
| Volume number/sequential designation |
v 197 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
1. Introduction --<br/> 2. Background --<br/> 3. Multigraph PETs --<br/> 4. The alternating grid system --<br/> 5. Outer billiards on semiregular octagons --<br/> 6. Quarter turn compositions --<br/> 7. Elementary properties --<br/> 8. Orbit stability and combinatorics --<br/> 9. Bilateral symmetry --<br/> 10. Proof of the main theorem --<br/> 11. The renormalization map --<br/> 12. Properties of the tiling --<br/> 13. The filling lemma --<br/> 14. The covering lemma --<br/> 15. Further geometric results --<br/> 16. Properties of the limit set --<br/> 17. Hausdorff convergence --<br/> 18. Recurrence relations --<br/> 19. Hausdorff dimension bounds --<br/> 20. Controlling the limit set --<br/> 21. The arc case - - 22. Further symmetries of the tiling --<br/> 23. The forest case --<br/> 24. The cantor set case --<br/> 25. Dynamics in the arc case --<br/> 26. Computational methods --<br/> 27. The calculations --<br/> 28. The raw data--<br/>Bibliography. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Polytopes. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Geometry. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Dynamical systems and ergodic theory -- Low-dimensional dynamical systems -- Universality, renormalization. |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Books |
