Abstract
The purpose of this article is to view the Penrose kite from the perspective of symplectic geometry.
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References
Atiyah M.: Convexity and Commuting Hamiltonians. Bull. London Math. Soc. 14, 1–15 (1982)
Battaglia F., Prato E.: The Symplectic Geometry of Penrose Rhombus Tilings. J. Symp. Geom. 6, 139–158 (2008)
Battaglia, F., Prato, E.: Ammann Tilings in Symplectic Geometry. http://arxiv.org/abs/1004.2471 [math.SG] (2010)
Cahn J.W.: Quasicrystals. J. Res. Natl. Inst. Stand. Technol. 106, 975–982 (2001)
Chen, W., Ruan, Y.: Orbifold Gromov–Witten theory. In: Orbifolds in mathematics and physics (Madison, WI, 2001), Contemp. Math. 310, 25–85, Providence, RI: Amer. Math. Soc., 2002, pp. 25–85
de Bruijn, N.G.: Algebraic Theory of Penrose’s Non–periodic Tilings of the Plane. Kon. Nederl. Akad. Wetensch. Proc. Ser. A 84, 39–52 and 53–66 (1981)
Delzant T.: Hamiltoniennes Périodiques et Image Convexe de l’Application Moment. Bull. S.M.F. 116, 315–339 (1988)
Guillemin V., Sternberg S.: Convexity Properties of the Moment Mapping. Invent. Math. 67, 491–513 (1982)
Livio M.: The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number. Broadway Books, New York (2003)
Penrose R.: The Rôle of Æsthetics in Pure and Applied Mathematical Research. Bull. Inst. Math. Appl. 10, 266–271 (1974)
Penrose R.: Pentaplexity. Math. Intelligencer 2, 32–38 (1979)
Prato E.: Simple Non–Rational Convex Polytopes via Symplectic Geometry. Topology 40, 961–975 (2001)
Prato, E.: The Pentagram: From the Goddess to Symplectic Geometry. Proc. Bridges 2007, Carmel, IN: Jacobs Publishing, 2007, pp. 123–126
Senechal M.: Quasicrystals and Geometry. Cambridge University Press, Cambridge (1995)
Shechtman D., Blech I., Gratias D., Cahn J.W.: Metallic Phase with Long–Range Orientational Order and no Translational Symmetry. Phys. Rev. Lett. 53, 1951–1953 (1984)
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Communicated by A. Connes
Research partially supported by MIUR (Geometria Differenziale e Analisi Globale, PRIN 2007).
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Battaglia, F., Prato, E. The Symplectic Penrose Kite. Commun. Math. Phys. 299, 577–601 (2010). https://doi.org/10.1007/s00220-010-1103-y
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DOI: https://doi.org/10.1007/s00220-010-1103-y