System dynamic of space euclidean and hyperbolic tilings - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T09:16:37Z http://mathoverflow.net/feeds/question/62934 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/62934/system-dynamic-of-space-euclidean-and-hyperbolic-tilings System dynamic of space euclidean and hyperbolic tilings tiep 2011-04-25T15:12:13Z 2011-04-25T15:25:37Z <p>Theorem 2.9. (Rudolph [Rud89]) Suppose \$X_{T}\$ is a finite local complexity (FLC) tiling space. Then \$X_{T}\$ is compact in the tiling metric d. Moreover, the action \$T\$ of \$R^{d}\$ by translation is on \$X_{T}\$ is continuous. -Probleme : We substitute \$R^{d}\$ par hyperbolic space \$H^{d}\$ ?? we can an answer positive?, in particular d=2,</p> <p>-Can you help me link to the proof of this theorem or the document: ++Daniel J. Rudolph, Rectangular tilings of \$R^{n}\$ and free \$R^{n}\$-actions, Dynamical systems (College Park, MD, 1986–87), Springer, Berlin, 1988, pp. 653–688. ++[Rud89] Daniel J. Rudolph, Markov tilings of \$R^{n}\$ and representations of \$R^{n}\$ actions, Measure and measurable dynamics (Rochester, NY, 1987), Amer. Math. Soc., Providence, RI, 1989, pp. 271–290. Merci beaucoup.</p> <p>cf.Symbolic Dynamics and Tilings of \$R^{d}\$. E. Arthur Robinson, Jr. [page 5] : <a href="http://home.gwu.edu/~robinson/Documents/AMS.pdf" rel="nofollow">http://home.gwu.edu/~robinson/Documents/AMS.pdf</a></p>