Citation: |
[1] |
N. E. J. De Bruijn, Algebraic theory of Penrose's nonperiodic tilings, Nederl. Akad. Wentensch. Proc., 84 (1981), 39-66. |
[2] |
R. Douady, "These de 3-Eme Cycle," Université de Paris 7, 1982. |
[3] |
D. Dolyopyat and B. Fayad, Unbounded orbits for semicircular outer billiards, Annales Henri Poincaré, 10 (2009), 357-375.doi: 10.1007/s00023-009-0409-9. |
[4] |
F. Dogru and S. Tabachnikov, Dual billiards, Math. Intelligencer, 27 (2005), 18-25. |
[5] |
K. J. Falconer, "Fractal Geometry: Mathematical Foundations and Applications," John Wiley & Sons, Ltd., Chichester, 1990. |
[6] |
D. Genin, "Regular and Chaotic Dynamics of Outer Billiards," Ph.D. thesis, The Pennsylvania State University, 2005. |
[7] |
E. Gutkin and N. Simányi, Dual polygonal billiard and necklace dynamics, Comm. Math. Phys., 143 (1992), 431-449.doi: 10.1007/BF02099259. |
[8] |
R. Kolodziej, The antibilliard outside a polygon, Bull. Pol. Acad Sci. Math., 37 (1989), 163-168. |
[9] |
L. Li, On Moser's boundedness problem of dual billiards, Ergodic Theorem and Dynamical Systems, 29 (2009), 613-635.doi: 10.1017/S0143385708000515. |
[10] |
J. Moser, Is the solar system stable?, Math. Intelligencer, 1 (1978/79), 65-71. doi: 10.1007/BF03023062. |
[11] |
J. Moser, "Stable and Random Motions in Dynamical Systems. With Special Emphasis on Celestial Mechanics," Hermann Weyl Lectures, the Institute for Advanced Study, Princeton, N.J., Ann. of Math. Stud., 77, Princeton University Press, Princeton, N.J., University of Tokyo Press, Tokyo, 1973. |
[12] |
B. H. Neumann, "Sharing Ham and Eggs," Summary of a Manchester Mathematics Colloquium, 25 Jan 1959, published in Iota, the Manchester University Mathematics Students' Journal. |
[13] |
R. E. Schwartz, Unbounded orbits for outer billiards, J. Mod. Dyn., 1 (2007), 371-424.doi: 10.3934/jmd.2007.1.371. |
[14] |
R. E. Schwartz, "Outer Billiards on Kites," Annals of Mathematics Studies, 171, Princeton University Press, Princeton, NJ, 2009. |
[15] |
R. E. Schwartz, Outer billiards and the pinwheel map, Journal of Modern Dynamics, 2011. |
[16] |
R. E. Schwartz, Outer Billiards, Quarter Turn Compositions, and Polytope Exchange Transformations, preprint, 2011. |
[17] |
S. Tabachnikov, "Geometry and Billiards," Student Mathematical Library, 30, Amer. Math. Soc., Providence, RI, Mathematics Advanced Study Semesters, University Park, PA, 2005. |
[18] |
S. Tabachnikov, "Billiards," Panoramas et Syntheses, 1, Société Mathématique de France, 1995. |
[19] |
F. Vivaldi and A. Shaidenko, Global stability of a class of discontinuous dual billiards, Comm. Math. Phys., 110 (1987), 625-640.doi: 10.1007/BF01205552. |