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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

Titel:	The Plaid Model: (AMS-198)
Verantwortlichkeitsangabe:	Richard Evan Schwartz
Autor/in / Beteiligte Person:	Schwartz, Richard Evan
Lokaler Link:	De Gruyter E-Books EBA bis 31.12.2026 (Volltext)
Link:	https://doi.org/10.1515/9780691188997 Cover
Verwandtes Werk:	Annals of Mathematics Studies
Veröffentlichung:	Princeton, NJ: Princeton University Press, [2019]
Medientyp:	Monographie
Datenträgertyp:	Elektronische Ressource
Umfang:	1 online resource (280 p.)
ISBN:	9780691188997
DOI:	10.1515/9780691188997
Schlagwort:	Combinatorial dynamics Differentiable dynamical systems Geometry Number theory Box Theorem Copy Lemma Copy Theorem Graph Reconstruction Lemma Grid Geometry Lemma Grid Supply Lemma Intertwining Lemma Matching Criterion Orbit Equivalence Theorem Projection Theorem Quasi-Isomorphism Theorem Rectangle Lemma Renormalization Theorem arithmetic alignment auxiliary lemmas capacity sequence equidistribution geometric alignment graph grid lemma map maps mass sequence number theory orbit outer billiards, planetary motion, planetary orbits, polytope exchange transformations, renormalization, continued fractions, corner percolation, Truchet tile system, plaid model, square tiling, plane, even rational parameter, capacities, masses, plaid polygons, parallel lines, grid lines, slanting lines, light point, symmetries, intersection points, capacity, light points, geometry, low capacity lines, polygon, scale information, 1-dimensional wordlines, remote adjacency, vertical particles, spacetime diagrams, Bad Tile Lemma, stacking blocks, pixilation, embedded loops, plaid polygon, spacetime plaid surfaces, pixelated spacetime diagrams, Curve Turning Theorem, particle lines, oriented lines, Truchet Comparison Theorem, pixelated spacetime, elementary number theory, fundamental surface, Plaid Master Picture Theorem, spaces, convex polytopes, checkerboard partition, Segment Lemma, anchor point, classifying map, vertical case, horizontal case, Vertical Lemma, symmetry, congruence, integer square, east edges, proof, Horizontal Lemma, technical lemma, prism structure, Graph Master Picture Theorem, Master Picture Theorem, special billiards orbits, kits, arithmetic graph, polytopes, Graph Master Theorem, convex polygon, kites, outer billiards map, compactification, quarter turn compositions, linear algebra, lemmas, theorems, PET, parallelotope plaid PET map prism sequences structural result MATHEMATICS / Geometry / General
Sonstiges:	Online-Ressource [Kann nicht per Fernleihe bestellt werden!] Gesamttitelangabe: Annals of Mathematics Studies ; 198 hbz Verbund-ID: HT020719213

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The Plaid Model: (AMS-198)