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024 7 $a10.1515/9781400831975
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035   $a(DE-B1597)9781400831975
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100   $a20090325d2009      uy             0
101 0 $aeng
135   $aur||#||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aOuter billiards on kites$b[electronic resource] /$fRichard Evan Schwartz
205   $aCourse Book
210   $aPrinceton, NJ $cPrinceton University Press$dc2009
215   $a1 online resource (321 p.)
225 1 $aAnnals of mathematics studies ;$v171
300   $aDescription based upon print version of record.
311   $a0-691-14248-3 
311   $a0-691-14249-1 
320   $aIncludes bibliographical references and index.
327   $tFront matter --$tContents --$tPreface --$tChapter 1. Introduction --$tPart 1. The Erratic Orbits Theorem --$tChapter 2. The Arithmetic Graph --$tChapter 3. The Hexagrid Theorem --$tChapter 4. Period Copying --$tChapter 5. Proof of the Erratic Orbits Theorem --$tPart 2. The Master Picture Theorem --$tChapter 6. The Master Picture Theorem --$tChapter 7. The Pinwheel Lemma --$tChapter 8. The Torus Lemma --$tChapter 9. The Strip Functions --$tChapter 10. Proof of the Master Picture Theorem --$tPart 3. Arithmetic Graph Structure Theorems --$tChapter 11. Proof of the Embedding Theorem --$tChapter 12. Extension and Symmetry --$tChapter 13. Proof of Hexagrid Theorem I --$tChapter 14. The Barrier Theorem --$tChapter 15. Proof of Hexagrid Theorem II --$tChapter 16. Proof of the Intersection Lemma --$tPart 4. Period-Copying Theorems --$tChapter 17. Diophantine Approximation --$tChapter 18. The Diophantine Lemma --$tChapter 19. The Decomposition Theorem --$tChapter 20. Existence of Strong Sequences --$tPart 5. The Comet Theorem --$tChapter 21. Structure of the Inferior and Superior Sequences --$tChapter 22. The Fundamental Orbit --$tChapter 23. The Comet Theorem --$tChapter 24. Dynamical Consequences --$tChapter 25. Geometric Consequences --$tPart 6. More Structure Theorems --$tChapter 26. Proof of the Copy Theorem --$tChapter 27. Pivot Arcs in the Even Case --$tChapter 28. Proof of the Pivot Theorem --$tChapter 29. Proof of the Period Theorem --$tChapter 30. Hovering Components --$tChapter 31. Proof of the Low Vertex Theorem --$tAppendix --$tBibliography --$tIndex
330   $aOuter billiards is a basic dynamical system defined relative to a convex shape in the plane. B. H. Neumann introduced this system in the 1950's, and J. Moser popularized it as a toy model for celestial mechanics. All along, the so-called Moser-Neumann question has been one of the central problems in the field. This question asks whether or not one can have an outer billiards system with an unbounded orbit. The Moser-Neumann question is an idealized version of the question of whether, because of small disturbances in its orbit, the Earth can break out of its orbit and fly away from the Sun. In Outer Billiards on Kites, Richard Schwartz presents his affirmative solution to the Moser-Neumann problem. He shows that an outer billiards system can have an unbounded orbit when defined relative to any irrational kite. A kite is a quadrilateral having a diagonal that is a line of bilateral symmetry. The kite is irrational if the other diagonal divides the quadrilateral into two triangles whose areas are not rationally related. In addition to solving the basic problem, Schwartz relates outer billiards on kites to such topics as Diophantine approximation, the modular group, self-similar sets, polytope exchange maps, profinite completions of the integers, and solenoids--connections that together allow for a fairly complete analysis of the dynamical system.
410  0$aAnnals of mathematics studies ;$v171.
606   $aHyperbolic spaces
606   $aSingularities (Mathematics)
606   $aTransformations (Mathematics)
606   $aGeometry, Plane
610   $aAbelian group.
610   $aAutomorphism.
610   $aBig O notation.
610   $aBijection.
610   $aBinary number.
610   $aBisection.
610   $aBorel set.
610   $aC0.
610   $aCalculation.
610   $aCantor set.
610   $aCartesian coordinate system.
610   $aCombination.
610   $aCompass-and-straightedge construction.
610   $aCongruence subgroup.
610   $aConjecture.
610   $aConjugacy class.
610   $aContinuity equation.
610   $aConvex lattice polytope.
610   $aConvex polytope.
610   $aCoprime integers.
610   $aCounterexample.
610   $aCyclic group.
610   $aDiameter.
610   $aDiophantine approximation.
610   $aDiophantine equation.
610   $aDisjoint sets.
610   $aDisjoint union.
610   $aDivision by zero.
610   $aEmbedding.
610   $aEquation.
610   $aEquivalence class.
610   $aErgodic theory.
610   $aErgodicity.
610   $aFactorial.
610   $aFiber bundle.
610   $aFibonacci number.
610   $aFundamental domain.
610   $aGauss map.
610   $aGeometry.
610   $aHalf-integer.
610   $aHomeomorphism.
610   $aHyperbolic geometry.
610   $aHyperplane.
610   $aIdeal triangle.
610   $aIntersection (set theory).
610   $aInterval exchange transformation.
610   $aInverse function.
610   $aInverse limit.
610   $aIsometry group.
610   $aLattice (group).
610   $aLimit set.
610   $aLine segment.
610   $aLinear algebra.
610   $aLinear function.
610   $aLine?line intersection.
610   $aMain diagonal.
610   $aModular group.
610   $aMonotonic function.
610   $aMultiple (mathematics).
610   $aOrthant.
610   $aOuter billiard.
610   $aParallelogram.
610   $aParameter.
610   $aPartial derivative.
610   $aPenrose tiling.
610   $aPermutation.
610   $aPiecewise.
610   $aPolygon.
610   $aPolyhedron.
610   $aPolytope.
610   $aProduct topology.
610   $aProjective geometry.
610   $aRectangle.
610   $aRenormalization.
610   $aRhombus.
610   $aRight angle.
610   $aRotational symmetry.
610   $aSanity check.
610   $aScientific notation.
610   $aSemicircle.
610   $aSign (mathematics).
610   $aSpecial case.
610   $aSquare root of 2.
610   $aSubsequence.
610   $aSummation.
610   $aSymbolic dynamics.
610   $aSymmetry group.
610   $aTangent.
610   $aTetrahedron.
610   $aTheorem.
610   $aToy model.
610   $aTranslational symmetry.
610   $aTrapezoid.
610   $aTriangle group.
610   $aTriangle inequality.
610   $aTwo-dimensional space.
610   $aUpper and lower bounds.
610   $aUpper half-plane.
610   $aWithout loss of generality.
610   $aYair Minsky.
615  0$aHyperbolic spaces.
615  0$aSingularities (Mathematics)
615  0$aTransformations (Mathematics)
615  0$aGeometry, Plane.
676   $a516.9
700   $aSchwartz$b Richard Evan$0307636
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910823888503321
996   $aOuter billiards on kites$9230026
997   $aUNINA