The Plaid Model: (AMS-198)
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About this ebook
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 the materials interactively and each theorem is accompanied by a computer demonstration.
Richard Evan Schwartz
Richard Evan Schwartz is professor of mathematics at Brown University and the author of Spherical CR Geometry and Dehn Surgery (Princeton).
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Knots, Groups and 3-Manifolds (AM-84), Volume 84: Papers Dedicated to the Memory of R.H. Fox. (AM-84) Rating: 0 out of 5 stars0 ratingsSmoothings of Piecewise Linear Manifolds. (AM-80), Volume 80 Rating: 5 out of 5 stars5/5Characteristic Classes. (AM-76), Volume 76 Rating: 5 out of 5 stars5/5Advances in the Theory of Riemann Surfaces. (AM-66), Volume 66 Rating: 0 out of 5 stars0 ratingsDiscrete Series of GLn Over a Finite Field. (AM-81), Volume 81 Rating: 0 out of 5 stars0 ratingsAutomorphic Forms on Adele Groups. (AM-83), Volume 83 Rating: 0 out of 5 stars0 ratingsInfinite Loop Spaces (AM-90), Volume 90: Hermann Weyl Lectures, The Institute for Advanced Study. (AM-90) Rating: 0 out of 5 stars0 ratingsThree-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110), Volume 110 Rating: 0 out of 5 stars0 ratingsSeminar on Singularities of Solutions of Linear Partial Differential Equations. (AM-91), Volume 91 Rating: 3 out of 5 stars3/5Braids, Links, and Mapping Class Groups. (AM-82), Volume 82 Rating: 0 out of 5 stars0 ratingsStrong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 Rating: 0 out of 5 stars0 ratingsScattering Theory for Automorphic Functions. (AM-87), Volume 87 Rating: 0 out of 5 stars0 ratingsMultiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105 Rating: 0 out of 5 stars0 ratingsFunctional Integration and Partial Differential Equations. (AM-109), Volume 109 Rating: 0 out of 5 stars0 ratingsRadically Elementary Probability Theory. (AM-117), Volume 117 Rating: 4 out of 5 stars4/5Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118 Rating: 0 out of 5 stars0 ratingsFoundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 Rating: 0 out of 5 stars0 ratingsEntire Holomorphic Mappings in One and Several Complex Variables. (AM-85), Volume 85 Rating: 0 out of 5 stars0 ratingsComplex Dynamics and Renormalization (AM-135), Volume 135 Rating: 4 out of 5 stars4/5Invariant Forms on Grassmann Manifolds. (AM-89), Volume 89 Rating: 0 out of 5 stars0 ratingsSeminar On Minimal Submanifolds. (AM-103), Volume 103 Rating: 0 out of 5 stars0 ratingsC*-Algebra Extensions and K-Homology. (AM-95), Volume 95 Rating: 0 out of 5 stars0 ratingsK-Theory of Forms. (AM-98), Volume 98 Rating: 0 out of 5 stars0 ratingsThe Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 Rating: 0 out of 5 stars0 ratingsNilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128 Rating: 0 out of 5 stars0 ratingsSimple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120), Volume 120 Rating: 0 out of 5 stars0 ratingsRecent Developments in Several Complex Variables. (AM-100), Volume 100 Rating: 0 out of 5 stars0 ratingsRandom Fourier Series with Applications to Harmonic Analysis. (AM-101), Volume 101 Rating: 0 out of 5 stars0 ratingsCosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121), Volume 121 Rating: 0 out of 5 stars0 ratings
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