The Plaid Model : : (AMS-198) /

The Plaid Model : : (AMS-198) / / Richard Evan Schwartz.

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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Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2019 English
VerfasserIn:
Schwartz, Richard Evan,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2019]
©2019
Year of Publication:2019
Language:English
Series:Annals of Mathematics Studies ; 198
Online Access:
Physical Description:1 online resource (280 p.)
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100 1 |a Schwartz, Richard Evan,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 4 |a The Plaid Model :  |b (AMS-198) /  |c Richard Evan Schwartz. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2019] 
264 4 |c ©2019 
300 |a 1 online resource (280 p.) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 0 |a Annals of Mathematics Studies ;  |v 198 
505 0 0 |t Frontmatter --   |t Contents --   |t Preface --   |t Introduction --   |t Part 1. The Plaid Model --   |t Chapter 1. Definition of the Plaid Model --   |t Chapter 2. Properties of the Model --   |t Chapter 3. Using the Model --   |t Chapter 4. Particles and Spacetime Diagrams --   |t Chapter 5. Three-Dimensional Interpretation --   |t Chapter 6. Pixellation and Curve Turning --   |t Chapter 7. Connection to the Truchet Tile System --   |t Part 2. The Plaid PET --   |t Chapter 8. The Plaid Master Picture Theorem --   |t Chapter 9. The Segment Lemma --   |t Chapter 10. The Vertical Lemma --   |t Chapter 11. The Horizontal Lemma --   |t Chapter 12. Proof of the Main Result --   |t Part 3. The Graph PET --   |t Chapter 13. Graph Master Picture Theorem --   |t Chapter 14. Pinwheels and Quarter Turns --   |t Chapter 15. Quarter Turn Compositions and PETs --   |t Chapter 16. The Nature of the Compactification --   |t Part 4. The Plaid-Graph Correspondence --   |t Chapter 17. The Orbit Equivalence Theorem --   |t Chapter 18. The Quasi-Isomorphism Theorem --   |t Chapter 19. Geometry of the Graph Grid --   |t Chapter 20. The Intertwining Lemma --   |t Part 5. The Distribution of Orbits --   |t Chapter 21. Existence of Infinite Orbits --   |t Chapter 22. Existence of Many Large Orbits --   |t Chapter 23. Infinite Orbits Revisited --   |t Chapter 24. Some Elementary Number Theory --   |t Chapter 25. The Weak and Strong Case --   |t Chapter 26. The Core Case --   |t References --   |t Index 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a 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 demo. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) 
650 0 |a Combinatorial dynamics. 
650 0 |a Differentiable dynamical systems. 
650 0 |a Geometry. 
650 0 |a Number theory. 
650 7 |a MATHEMATICS / Geometry / General.  |2 bisacsh 
653 |a 1-dimensional wordlines. 
653 |a Bad Tile Lemma. 
653 |a Box Theorem. 
653 |a Copy Lemma. 
653 |a Copy Theorem. 
653 |a Curve Turning Theorem. 
653 |a Graph Master Picture Theorem. 
653 |a Graph Master Theorem. 
653 |a Graph Reconstruction Lemma. 
653 |a Grid Geometry Lemma. 
653 |a Grid Supply Lemma. 
653 |a Horizontal Lemma. 
653 |a Intertwining Lemma. 
653 |a Master Picture Theorem. 
653 |a Matching Criterion. 
653 |a Orbit Equivalence Theorem. 
653 |a PET. 
653 |a Plaid Master Picture Theorem. 
653 |a Projection Theorem. 
653 |a Quasi-Isomorphism Theorem. 
653 |a Rectangle Lemma. 
653 |a Renormalization Theorem. 
653 |a Segment Lemma. 
653 |a Truchet Comparison Theorem. 
653 |a Truchet tile system. 
653 |a Vertical Lemma. 
653 |a anchor point. 
653 |a arithmetic alignment. 
653 |a arithmetic graph. 
653 |a auxiliary lemmas. 
653 |a capacities. 
653 |a capacity sequence. 
653 |a capacity. 
653 |a checkerboard partition. 
653 |a classifying map. 
653 |a compactification. 
653 |a congruence. 
653 |a continued fractions. 
653 |a convex polygon. 
653 |a convex polytopes. 
653 |a corner percolation. 
653 |a east edges. 
653 |a elementary number theory. 
653 |a embedded loops. 
653 |a equidistribution. 
653 |a even rational parameter. 
653 |a fundamental surface. 
653 |a geometric alignment. 
653 |a geometry. 
653 |a graph grid. 
653 |a grid lines. 
653 |a horizontal case. 
653 |a integer square. 
653 |a intersection points. 
653 |a kites. 
653 |a kits. 
653 |a lemma. 
653 |a lemmas. 
653 |a light point. 
653 |a light points. 
653 |a linear algebra. 
653 |a low capacity lines. 
653 |a map. 
653 |a maps. 
653 |a mass sequence. 
653 |a masses. 
653 |a number theory. 
653 |a orbit. 
653 |a oriented lines. 
653 |a outer billiards map. 
653 |a outer billiards. 
653 |a parallel lines. 
653 |a parallelotope. 
653 |a particle lines. 
653 |a pixelated spacetime diagrams. 
653 |a pixelated spacetime. 
653 |a pixilation. 
653 |a plaid PET map. 
653 |a plaid model. 
653 |a plaid polygon. 
653 |a plaid polygons. 
653 |a plane. 
653 |a planetary motion. 
653 |a planetary orbits. 
653 |a polygon. 
653 |a polytope exchange transformations. 
653 |a polytopes. 
653 |a prism structure. 
653 |a prism. 
653 |a proof. 
653 |a quarter turn compositions. 
653 |a remote adjacency. 
653 |a renormalization. 
653 |a scale information. 
653 |a sequences. 
653 |a slanting lines. 
653 |a spaces. 
653 |a spacetime diagrams. 
653 |a spacetime plaid surfaces. 
653 |a special billiards orbits. 
653 |a square tiling. 
653 |a stacking blocks. 
653 |a structural result. 
653 |a symmetries. 
653 |a symmetry. 
653 |a technical lemma. 
653 |a theorems. 
653 |a vertical case. 
653 |a vertical particles. 
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773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press Complete eBook-Package 2019  |z 9783110663365 
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