Screen LibraryThe plaid model /
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 bill...
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| Main Authors: | |
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| Published: |
Princeton University Press,
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| Publisher Address: | Princeton, New Jersey : |
| Publication Dates: | 2019. |
| Literature type: | Book |
| Language: | English |
| Series: |
Annals of mathematics studies ;
number 198 |
| Subjects: | |
| Summary: |
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, c |
| Carrier Form: | xii, 268 pages : illustrations ; 25 cm. |
| Bibliography: | Includes bibliographical references (page 265) and index. |
| ISBN: |
9780691181370 0691181373 9780691181387 0691181381 |
| Index Number: | QA614 |
| CLC: | O193 |
| Call Number: | O193/S399 |
| Contents: |
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 |