Non-Unimodularity

Sing, Bernd

Actes des rencontres du CIRM, Tome 1 (2009) no. 1, pp. 69-74.

[1] S. Akiyama. “Finiteness and periodicity of beta expansions – number theoretical and dynamical open problems”. Talk given at the Conference “Numeration: Mathematics and Computer Science”, held at the CIRM, Luminy, France, from March 23 to 27, 2009; see this volume. | DOI | Zbl

[2] M. Baake. “A guide to mathematical quasicrystals”. In: J.-B. Suck, M. Schreiber, and P. Häussler (editors), Quasicrystals: An Introduction to Structure, Physical Properties, and Applications, Springer Series in Materials Science 55. Springer, Berlin, 2002, pages 17–48. | arXiv | DOI

[3] M. Baake, R.V. Moody, and M. Schlottmann. “Limit-(quasi)periodic point sets as quasicrystals with $p$-adic internal spaces”. J. Phys. A: Math. Gen. 31(27):5755–5765 (1998). | arXiv | DOI | Zbl

[4] L’. Balková. “Resemblance and difference between beta-integers and ordinary integers”. Talk given at the Conference “Numeration: Mathematics and Computer Science”, held at the CIRM, Luminy, France, from March 23 to 27, 2009; see this volume. | DOI | MR

[5] M. Barge and J. Kwapisz. “Geometric theory of unimodular Pisot substitutions”. Amer. J. Math. 128(5):1219–1282 (2006). | DOI | MR | Zbl

[6] F. Durand. “Rauzy fractal in $ℝ\times ℂ$ and points with multiple expansions”. Talk given at the Conference “Numeration: Mathematics and Computer Science”, held at the CIRM, Luminy, France, from March 23 to 27, 2009; see this volume.

[7] F. Durand and A. Messaoudi. “Boundary of the Rauzy fractal sets in $ℝ\times ℂ$ generated by $P\left(x\right)=x^4-x^3-x^2-x-1$”. Preprint. | Zbl

[8] S. Ito and H. Rao. “Atomic surfaces, tilings and coincidence I. Irreducible case”. Israel J. Math. 153:129–156 (2006). | DOI | MR | Zbl

[9] R.V. Moody. “Model sets: a survey”. In: F. Axel, F. Dénoyer, and J.P. Gazeau (editors), From Quasicrystals to More Complex Systems. Winter School “Order, Chance and Risk: Aperiodic Phenomena from Solid State to Finance”, held at Centre de Physique Les Houches, France, from February 23 to March 6, 1998. Centre de Physique des Houches 13. Springer, Berlin, 2000, pages 145–166. | arXiv | DOI

[10] M. Schlottmann. “Cut-and-project sets in locally compact Abelian groups”. In: J. Patera (editor), Quasicrystals and Discrete Geometry. 1995 Fall Programme at The Fields Institute, Toronto, ON, Canada. Fields Institute Monographs 10. American Mathematical Society, Providence, RI, 1998, pages 247–264. | DOI | Zbl

[11] A. Siegel. “Represéntation des systèmes dynamiques substitutifs non unimodulaires”. Ergodic Theory Dynam. Systems 23(4):1247–1273 (2003). | DOI

[12] A. Siegel. “Pure discrete spectrum dynamical system and periodic tiling associated with a substitution”. Ann. Inst. Fourier (Grenoble) 54(2):288–299 (2004). | Numdam | Zbl

[13] B. Sing. Pisot Substitutions and Beyond. PhD thesis, Universität Bielefeld, 2007. Available at http://nbn-resolving.de/urn/resolver.pl?urn=urn:nbn:de:hbz:361-11555.