OUTER BILLIARDS ON KITES

By SARAH HERNANDEZ

PART I 2 THE ARITHMETIC GRAPH 3 ERRATIC ORBITS ALMOST ALWAYS 4 THE HEXAGRID THEOREM 5 ADDITIONAL STRUCTURE OF THE GRAPH 6 ODD RATIONAL APPROXIMATION 7 PERIOD COPYING 8 THE MAIN RESULTS 9 FURTHER RESULTS AND CONJECTURES PART II 10 THE MASTER PICTURE THEOREM 11 THE PINWHEEL LEMMA 12 THE TORUS LEMMA 13 THE STRIP FUNCTIONS 14 PROOF OF THE MASTER PICTURE THEOREM 15 SOME FORMULAS PART III 16 PROOF OF THE EMBEDDING THEOREM 17 EXTENSION AND SYMMETRY 18 THE ODD HEXAGRID THEOREM I 19 THE ODD HEXAGRID THEOREM II 20 THE EVEN HEXAGRID THEOREM PART IV 21 PROOF OF THE COPY THEOREM 22 THE INDUCTION LEMMA 23 DECOMPOSITION THEOREM: THE BASE CASE 24 PROOF OF THE DECOMPOSITION THEOREM 25 REFERENCES