Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.
We prove the existence of a topologically mixing interval exchange transformation and prove that no interval exchange is topologically mixing of all orders.
[1]Apostol, T.. Introduction to Analytic Number Theory. Springer, Berlin, 1976.Google Scholar
[2]
[2]Avila, A. and Forni, G.. Weak mixing for interval exchange transformations and translation flows. Ann. of Math. (2)165(2) (2007), 637–664.CrossRefGoogle Scholar
[3]
[3]Boshernitzan, M. and Chaika, J.. Diophantine properties of IETs and general systems: quantitative proximality and connectivity. Preprint, arXiv: 0910.5422.Google Scholar
[4]
[4]Boshernitzan, M. and Nogueira, A.. Generalized eigenfunctions of interval exchange maps. Ergod. Th. & Dynam. Sys.24(3) (2004), 697–705.CrossRefGoogle Scholar
[5]
[5]Chaika, J., Damanik, D. and Krueger, H.. Schrodinger operators defined by interval exchange transformations. J. Mod. Dyn.3(2) (2009), 253–270.Google Scholar
[6]
[6]Chaves, J. and Nogueira, A.. Spectral properties of interval exchange maps. Monatsh. Math.134(2) (2001), 89–102.CrossRefGoogle Scholar
[7]
[7]Dekking, F. M. and Keane, M.. Mixing properties of substitutions. Z. Wahrschein. Verw. Gebiete42(1) (1978), 23–33.CrossRefGoogle Scholar