Algebraic & Geometric Topology Volume 15, issue 4 (2015)

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Ellis enveloping semigroup for almost canonical model sets of an Euclidean space

Jean-Baptiste Aujogue

Algebraic & Geometric Topology 15 (2015) 2195–2237

DOI: 10.2140/agt.2015.15.2195

Bibliography

1	J B Aujogue, On embedding Meyer multiple sets into model multiple sets (2014) arXiv:1405.3013
2	J Auslander, Minimal flows and their extensions, Mathematics Studies 153, North-Holland (1988) MR956049
3	M Baake, J Hermisson, P A B Pleasant, The torus parametrization of quasiperiodic LI–classes, J. Physics 30 (1997)
4	M Baake, D Lenz, Dynamical systems on translation bounded measures: Pure point dynamical and diffraction spectra, Ergodic Theory Dynam. Systems 24 (2004) 1867 MR2106769
5	M Baake, D Lenz, R V Moody, Characterization of model sets by dynamical systems, Ergodic Theory Dynam. Systems 27 (2007) 341 MR2308136
6	K S Brown, Semigroups, rings, and Markov chains, J. Theoret. Probab. 13 (2000) 871 MR1785534
7	R Ellis, W H Gottschalk, Homomorphisms of transformation groups, Trans. Amer. Math. Soc. 94 (1960) 258 MR0123635
8	A H Forrest, J R Hunton, J Kellendonk, Cohomology of canonical projection tilings, Comm. Math. Phys. 226 (2002) 289 MR1892456
9	F Gähler, J Hunton, J Kellendonk, Integral cohomology of rational projection method patterns, Algebr. Geom. Topol. 13 (2013) 1661 MR3071138
10	E Glasner, On tame dynamical systems, Colloquium Math. 105 (2006) 283 MR2237913
11	E Glasner, Enveloping semigroups in topological dynamics, Topology Appl. 154 (2007) 2344 MR2328017
12	E Glasner, The structure of tame minimal dynamical systems, Ergodic Theory Dynam. Systems 27 (2007) 1819 MR2371597
13	E Glasner, M Megrelishvili, Hereditarily non-sensitive dynamical systems and linear representations, Colloq. Math. 104 (2006) 223 MR2197078
14	E Glasner, M Megrelishvili, V V Uspenskij, On metrizable enveloping semigroups, Israel J. Math. 164 (2008) 317 MR2391152
15	A Hof, On diffraction by aperiodic structures, Comm. Math. Phys. 169 (1995) 25 MR1328260
16	A Julien, Complexity and cohomology for cut-and-projection tilings, Ergodic Theory Dynam. Systems 30 (2010) 489 MR2599890
17	J Kellendonk, L Sadun, Meyer sets, eigenvalues, and Cantor fiber bundles, J. London Math. Soc. (2013)
18	J L Kelley, General topology, Van Nostrand (1955) MR0070144
19	T T Q Le, Local rules for quasiperiodic tilings, from: "The mathematics of long-range aperiodic order" (editor R V Moody), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 489, Kluwer (1997) 331 MR1460029
20	J Y Lee, R V Moody, A characterization of model multi-colour sets, Ann. Henri Poincaré 7 (2006) 125 MR2205466
21	J Y Lee, R V Moody, B Solomyak, Pure point dynamical and diffraction spectra, Ann. Henri Poincaré 3 (2002) 1003 MR1937612
22	J Y Lee, B Solomyak, Pisot family self-affine tilings, discrete spectrum, and the Meyer property, Discrete Contin. Dyn. Syst. 32 (2012) 935 MR2851885
23	R V Moody, Meyer sets and their duals, from: "The mathematics of long-range aperiodic order" (editor R V Moody), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 489, Kluwer (1997) 403 MR1460032
24	R V Moody, Model sets: A survey, from: "Quasicrystals to more complex systems" (editors F Axel, F Dénoyer, J P Gazeau), Springer (2000) 145
25	R V Moody, Mathematical quasicrystals: A tale of two topologies, from: "XIV International Congress on Mathematical Physics" (editor J C Zambrini), World Scientific (2005) 68 MR2227822
26	R Pikula, Enveloping semigroups of affine skew products and Sturmian-like systems, PhD thesis, Ohio State University (2009) MR2713787
27	I F Putnam, Non-commutative methods for the $K$–theory of $C^$–algebras of aperiodic patterns from cut-and-project systems*, Comm. Math. Phys. 294 (2010) 703 MR2585984
28	F V Saliola, The face semigroup algebra of a hyperplane arrangement, Canad. J. Math. 61 (2009) 904 MR2541389
29	M Schlottmann, Generalized model sets and dynamical systems, from: "Directions in mathematical quasicrystals" (editors M Baake, R V Moody), CRM Monogr. 13, Amer. Math. Soc. (2000) 143 MR1798991
30	M Senechal, Quasicrystals and geometry, Cambridge Univ. Press (1995) MR1340198
31	W A Veech, Point-distal flows, Amer. J. Math. 92 (1970) 205 MR0267560