References
- [Adler et al. 01] R. Adler, B. Kitchens, and C. Tresser. “Dynamics of Non-Ergodic Piecewise Affine Maps of the Torus.” Ergodic Theory Dyn. Syst. 21: 4 (2001), 959–999.
- [Akiyama and Harriss 13] S. Akiyama and E. Harriss. “Pentagonal Domain Exchange.” Discrete Contin. Dyn. Syst. 33: 10 (2013), 4375–4400.
- [Bedaride and Bertazzon 16] N. Bedaride and J.-F. Bertazzon. “An Example of Pet. Computation of the Hausdorff Dimension of the Aperiodic Set.” Trans. AMS. (2016), 357–391.
- [Buzzi 01] J. Buzzi. “Piecewise Isometries have Zero Topological Entropy.” Ergodic Theory Dyn. Syst. 21: 5 (2001), 1371–1377.
- [Falconer 14] K. Falconer. Fractal Geometry: Mathematical Foundations and Applications, third edition. Chichester: John Wiley & Sons, Ltd., 2014.
- [Goetz 00] A. Goetz. “Dynamics of Piecewise Isometries.” Illinois J. Math. 44: 3 (2000), 465–478.
- [Goetz 03] A. Goetz. “Piecewise Isometries-An Emerging Area of Dynamical Systems.” In Fractals in Graz 2001, Trends Math., edited by P. Grabner and W. Woess, pp. 135–144. Basel: Birkhäuser, 2003.
- [Goetz and Poggiaspalla 04] A. Goetz and G. Poggiaspalla. “Rotations by π/7.” Nonlinearity 17: 5 (2004), 1787–1802.
- [Gutkin and Haydn 97] E. Gutkin and N. Haydn. “Topological Entropy of Polygon Exchange Transformations and Polygonal Billiards.” Ergodic Theory Dyn. Syst. 17: 4 (1997), 849–867.
- [Haller 81] H. Haller. “Rectangle Exchange Transformations.” Monatsh. Math. 91: 3 (1981), 215–232.
- [Hooper 13] P. Hooper. “Renormalization of Polygon Exchange Maps Arising from Corner Percolation.” Invent. Math. 191: 2 (2013), 255–320.
- [Keane 75] M. Keane. “Interval Exchange Transformations.” Math. Z. 141 (1975), 25–31.
- [Lowenstein 07] J. H. Lowenstein. “Aperiodic Orbits of Piecewise Rational Rotations of Convex Polygons with Recursive Tiling.” Dyn. Syst. 22: 1 (2007), 25–63.
- [Lowenstein et al. 04] J. H. Lowenstein, K. L. Kouptsov, and F. Vivaldi. “Recursive Tiling and Geometry of Piecewise Rotations by π/7.” Nonlinearity 17: 2 (2004), 371–395.
- [Rauzy 79] G. Rauzy. “Échanges d’intervalles et Transformations Induites.” Acta Arith. 34: 4 (1979), 315–328.
- [Schwartz 14] R. E. Schwartz. The Octagonal PETs, Mathematical Surveys and Monographs, vol. 197. Providence, RI: American Mathematical Society, 2014.
- [Tabachnikov 95] S. Tabachnikov. “On the Dual Billiard Problem.” Adv. Math. 115: 2 (1995), 221–249.
- [Viana 06] M. Viana. “Ergodic Theory of Interval Exchange Maps.” Rev. Mat. Complut. 19: 1 (2006), 7–100.
- [Yoccoz 06] J-C. Yoccoz. “Continued Fraction Algorithms for Interval Exchange Maps: An Introduction.” In Frontiers in Number Theory, Physics, and Geometry. I, edited by P.E. Cartier, B. Julia, P. Moussa, and P. Vanhove, pp. 401–435. Berlin: Springer, 2006.
- [Zorich 06] A. Zorich. “Flat Surfaces.” In Frontiers in Number Theory, Physics, and Geometry. I, edited by P.E. Cartier, B. Julia, P. Moussa, and P. Vanhove, pp. 437–583. Berlin: Springer, 2006.