Geodesic
Anzai and Furstenberg Transformations on the 2-Torus and Topologically Quasi-Discrete Spectrum
Canadian mathematical bulletin, Tome 38 (1995) no. 1, pp. 87-92

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Let φ0 be an Anzai transformation on the 2-torus T2 defined by φ0(x,y) = (e2πiθx,xy) and φy a Furstenberg transformation on T2 defined by φf(x,y) = (e2πiθx,e2πif(x)xy) where θ is an irrational number and f is a real valued continuous function on the 1-torus T. In the present note we will show that φf has topologically quasi-discrete spectrum if and only if φf is topologically conjugate to φ0. Furthermore we will show that for any irrational number θ there is a real valued continuous function f on T such that φf does not have topologically quasi-discrete spectrum but is uniquely ergodic.
DOI : 10.4153/CMB-1995-011-1
Mots-clés : 46L80, 46L40 
Kodaka, Kazunori. Anzai and Furstenberg Transformations on the 2-Torus and Topologically Quasi-Discrete Spectrum. Canadian mathematical bulletin, Tome 38 (1995) no. 1, pp. 87-92. doi: 10.4153/CMB-1995-011-1
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     title = {Anzai and {Furstenberg} {Transformations} on the {2-Torus} and {Topologically} {Quasi-Discrete} {Spectrum}},
     journal = {Canadian mathematical bulletin},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-011-1/}
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