Cover Image

Outer billiards on kites /

"Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B. H. Neumann introduced this system in the 1950s, 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 proble...

Full description

Bibliographic Details
Main Author: Schwartz, Richard Evan
Format: Book
Language:English
Published: Princeton : Princeton University Press, 2009.
Series:Annals of mathematics studies ; no. 171.
Subjects:
Hyperbolic spaces.
Singularities (Mathematics)
Transformations (Mathematics)
Geometry, Plane.
Table of Contents:
  • Introduction
  • The arithmetic graph
  • The hexagrid theorem
  • Period copying
  • Proof of the erratic orbits theorem
  • The master picture theorem
  • The pinwheel lemma
  • The torus lemma
  • The strip functions
  • Proof of the master picture theorem - Proof of the embedding theorem
  • Extension and symmetry
  • Proof of hexagrid theorem I
  • The barrier theorem
  • Proof of hexagrid theorem II
  • Proof of the intersection lemma
  • Diophantine approximation
  • The diophantine lemma
  • The decomposition theorem
  • Existence of strong sequences
  • Structure of the inferior and superior sequences
  • The comet theorem
  • Dynamical consequences
  • Geometric consequences
  • Proof of the copy theorem
  • Pivot arcs in the even case
  • Proof of the pivot theorem
  • Proof of the period theorem
  • Hovering components
  • Proof of the low vertex theorem
  • Structure of periodic points
  • Self-similarity
  • General orbits on kites
  • General quadrilaterals.