Topological spectrum of locally compact Cantor minimal systems
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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
- Jon Aaronson, The eigenvalues of nonsingular transformations, Israel J. Math. 45 (1983), no. 4, 297–312. MR 720305, DOI 10.1007/BF02804014
- Jon Aaronson and Mahendra Nadkarni, $L_\infty$ eigenvalues and $L_2$ spectra of nonsingular transformations, Proc. London Math. Soc. (3) 55 (1987), no. 3, 538–570. MR 907232, DOI 10.1112/plms/s3-55.3.538
- Alexandre I. Danilenko, Strong orbit equivalence of locally compact Cantor minimal systems, Internat. J. Math. 12 (2001), no. 1, 113–123. MR 1812067, DOI 10.1142/S0129167X0100068X
- Thierry Giordano, Ian F. Putnam, and Christian F. Skau, Topological orbit equivalence and $C^*$-crossed products, J. Reine Angew. Math. 469 (1995), 51–111. MR 1363826
- Bernard Host, Jean-François Méla, and François Parreau, Nonsingular transformations and spectral analysis of measures, Bull. Soc. Math. France 119 (1991), no. 1, 33–90 (English, with French summary). MR 1101939
- Y. Ito, T. Kamae, and I. Shiokawa, Point spectrum and Hausdorff dimension, Number theory and combinatorics. Japan 1984 (Tokyo, Okayama and Kyoto, 1984) World Sci. Publishing, Singapore, 1985, pp. 209–227. MR 827785
- Matui, H.; Topological orbit equivalence of locally compact Cantor minimal systems, Ergodic Theory Dynam. Systems 22 (2002), 1871–1903.
- S. M. Srivastava, A course on Borel sets, Graduate Texts in Mathematics, vol. 180, Springer-Verlag, New York, 1998. MR 1619545, DOI 10.1007/978-3-642-85473-6
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
- Received by editor(s): April 12, 2002
- Published electronically: August 21, 2003
- Communicated by: Michael Handel
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 87-95
- MSC (2000): Primary 37B05
- DOI: https://doi.org/10.1090/S0002-9939-03-07239-3
- MathSciNet review: 2021251