소장자료
LDR | 04307nam a2200000 a | ||
001 | 0100414485▲ | ||
003 | OCoLC▲ | ||
005 | 20190716132037▲ | ||
007 | ta ▲ | ||
008 | 180910s2019 njua b 001 0 eng c▲ | ||
020 | ▼a9780691181370 (hbk.)▲ | ||
020 | ▼a0691181373 (hbk.)▲ | ||
020 | ▼a9780691181387 (pbk.)▲ | ||
020 | ▼a0691181381 (pbk.)▲ | ||
020 | ▼z9780691188997 (ebk.)▲ | ||
035 | ▼a(OCoLC)1051133975▼z(OCoLC)1051136278▲ | ||
040 | ▼aYDX▼beng▼cYDX▼dOCLCQ▼dTFW▼dYDXIT▼dOCLCF▼dMTG▼dORE▼dBUB▼dOCL▲ | ||
082 | 0 | 4 | ▼a515/.39▼223▲ |
090 | ▼a515.39▼bS399p▲ | ||
100 | 1 | ▼aSchwartz, Richard Evan.▲ | |
245 | 1 | 4 | ▼aThe plaid model /▼cRichard Evan Schwartz.▲ |
260 | ▼aPrinceton :▼bPrinceton University Press,▼c2019.▲ | ||
300 | ▼axii, 268 p. :▼bill. ;▼c25 cm.▲ | ||
490 | 0 | ▼aAnnals of mathematics studies ;▼vn. 198▲ | |
504 | ▼aIncludes bibliographical references (p. 265) and index.▲ | ||
505 | 0 | 0 | ▼tFrontmatter --▼tContents --▼tPreface --▼tIntroduction --▼tPart 1. The Plaid Model --▼tChapter 1. Definition of the Plaid Model --▼tChapter 2. Properties of the Model --▼tChapter 3. Using the Model --▼tChapter 4. Particles and Spacetime Diagrams --▼tChapter 5. Three-Dimensional Interpretation --▼tChapter 6. Pixellation and Curve Turning --▼tChapter 7. Connection to the Truchet Tile System --▼tPart 2. The Plaid PET --▼tChapter 8. The Plaid Master Picture Theorem --▼tChapter 9. The Segment Lemma --▼tChapter 10. The Vertical Lemma --▼tChapter 11. The Horizontal Lemma --▼tChapter 12. Proof of the Main Result --▼tPart 3. The Graph PET --▼tChapter 13. Graph Master Picture Theorem --▼tChapter 14. Pinwheels and Quarter Turns --▼tChapter 15. Quarter Turn Compositions and PETs --▼tChapter 16. The Nature of the Compactification --▼tPart 4. The Plaid-Graph Correspondence --▼tChapter 17. The Orbit Equivalence Theorem --▼tChapter 18. The Quasi-Isomorphism Theorem --▼tChapter 19. Geometry of the Graph Grid --▼tChapter 20. The Intertwining Lemma --▼tPart 5. The Distribution of Orbits --▼tChapter 21. Existence of Infinite Orbits --▼tChapter 22. Existence of Many Large Orbits --▼tChapter 23. Infinite Orbits Revisited --▼tChapter 24. Some Elementary Number Theory --▼tChapter 25. The Weak and Strong Case --▼tChapter 26. The Core Case --▼tReferences --▼tIndex▲ |
520 | ▼aOuter billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. The Plaid Model, which is a self-contained sequel to Richard Schwartz's Outer Billiards on Kites, provides a combinatorial model for orbits of outer billiards on kites. Schwartz relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called "the plaid model," has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics.The book includes an extensive computer program that allows readers to explore materials interactively and each theorem is accompanied by a computer demonstration.▲ | ||
650 | 0 | ▼aDifferentiable dynamical systems.▲ | |
650 | 0 | ▼aCombinatorial dynamics.▲ | |
650 | 0 | ▼aGeometry.▲ | |
650 | 0 | ▼aNumber theory.▲ |
![](https://lib.pusan.ac.kr/wp-content/themes/pnul2022/assets/images/default/default_w_279X393.png)
The plaid model
자료유형
국외단행본
서명/책임사항
The plaid model / Richard Evan Schwartz.
발행사항
Princeton : Princeton University Press , 2019.
형태사항
xii, 268 p. : ill. ; 25 cm.
총서사항
Annals of mathematics studies ; n. 198
서지주기
Includes bibliographical references (p. 265) and index.
내용주기
Frontmatter -- Contents -- Preface -- Introduction -- Part 1. The Plaid Model -- Chapter 1. Definition of the Plaid Model -- Chapter 2. Properties of the Model -- Chapter 3. Using the Model -- Chapter 4. Particles and Spacetime Diagrams -- Chapter 5. Three-Dimensional Interpretation -- Chapter 6. Pixellation and Curve Turning -- Chapter 7. Connection to the Truchet Tile System -- Part 2. The Plaid PET -- Chapter 8. The Plaid Master Picture Theorem -- Chapter 9. The Segment Lemma -- Chapter 10. The Vertical Lemma -- Chapter 11. The Horizontal Lemma -- Chapter 12. Proof of the Main Result -- Part 3. The Graph PET -- Chapter 13. Graph Master Picture Theorem -- Chapter 14. Pinwheels and Quarter Turns -- Chapter 15. Quarter Turn Compositions and PETs -- Chapter 16. The Nature of the Compactification -- Part 4. The Plaid-Graph Correspondence -- Chapter 17. The Orbit Equivalence Theorem -- Chapter 18. The Quasi-Isomorphism Theorem -- Chapter 19. Geometry of the Graph Grid -- Chapter 20. The Intertwining Lemma -- Part 5. The Distribution of Orbits -- Chapter 21. Existence of Infinite Orbits -- Chapter 22. Existence of Many Large Orbits -- Chapter 23. Infinite Orbits Revisited -- Chapter 24. Some Elementary Number Theory -- Chapter 25. The Weak and Strong Case -- Chapter 26. The Core Case -- References -- Index
요약주기
Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. The Plaid Model, which is a self-contained sequel to Richard Schwartz's Outer Billiards on Kites, provides a combinatorial model for orbits of outer billiards on kites. Schwartz relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called "the plaid model," has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics.The book includes an extensive computer program that allows readers to explore materials interactively and each theorem is accompanied by a computer demonstration.
ISBN
9780691181370 (hbk.) 0691181373 (hbk.) 9780691181387 (pbk.) 0691181381 (pbk.)
청구기호
515.39 S399p
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