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Topological spectrum of locally compact Cantor minimal systems

Author(s): Hiroki Matui
Journal: Proc. Amer. Math. Soc. 132 (2004), 87-95.
MSC (2000): Primary 37B05
Posted: August 21, 2003
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Abstract: We show that there exists a locally compact Cantor minimal system whose topological spectrum has a given Hausdorff dimension.

References:

[A]
Aaronson, J.; The eigenvalues of nonsingular transformations, Israel J. Math. 45 (1983), 297-312. MR 86c:28041

[AN]
Aaronson, J.; Nadkarni, M.; $L_{\infty}$ eigenvalues and $L_2$ spectra of nonsingular transformations, Proc. London Math. Soc. (3) 55 (1987), 538-570. MR 88j:28012

[D]
Danilenko, A. I.; Strong orbit equivalence of locally compact Cantor minimal systems, Internat. J. Math. 12 (2001), 113-123. MR 2002j:37016

[GPS]
Giordano, T.; Putnam, I. F.; Skau, C. F.; Topological orbit equivalence and $C^*$-crossed products, J. reine angew. Math. 469 (1995), 51-111. MR 97g:46085

[HMP]
Host, B.; Mela, J.-F.; Parreau, F.; Nonsingular transformations and spectral analysis of measures, Bull. Soc. Math. France 119 (1991), 33-90. MR 93d:43002

[IKS]
Ito, Y.; Kamae, T.; Shiokawa, I.; Point spectrum and Hausdorff dimension, Number theory and combinatorics (Japan 1984), 209-227, World Sci. Publishing, Singapore, 1985. MR 87h:28018

[M]
Matui, H.; Topological orbit equivalence of locally compact Cantor minimal systems, Ergodic Theory Dynam. Systems 22 (2002), 1871-1903.

[S]
Srivastava, S. M.; A course on Borel sets, Graduate Texts in Mathematics 180, Springer-Verlag, New York, 1998. MR 99d:04002

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Additional Information:

Hiroki Matui
Affiliation: Department of Mathematics and Informatics, Faculty of Science, Chiba University, Yayoityô 1-33, Inageku, Chiba, 263-8522, Japan
Email: matui@math.s.chiba-u.ac.jp

DOI: 10.1090/S0002-9939-03-07239-3
PII: S 0002-9939(03)07239-3
Received by editor(s): April 12, 2002
Posted: August 21, 2003
Communicated by: Michael Handel
Copyright of article: Copyright 2003, American Mathematical Society

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