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Odometer action on Riesz product

Published online by Cambridge University Press:  09 April 2009

Masamichi Yoshida
Affiliation:
Department of Mathematics Osaka City UniversitySugimoto, Sumiyoshi-ku Osaka, Japan
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Abstract

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We consider the Riesz product with a constant coefficient and odometer action over infinite product spaces. By studying the ratio set we can conclude the type of the above dynamical systems is III1.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Brown, G. and Dooley, A. H., ‘Odometer actions and G-measures’, Ergodic Theory Dynamical Systems 11 (1991), 279307.CrossRefGoogle Scholar
[2]Brown, G., ‘Riesz products and generalized characters’, Proc. London Math. Soc. 30 (1975), 209238.CrossRefGoogle Scholar
[3]Brown, G., Dooley, A. H. and Lake, J., ‘On the Krieger-Araki-Woods ratio set’, preprint.CrossRefGoogle Scholar
[4]Hamachi, T., Oka, Y. and Osikawa, M., ‘A classification of ergodic nonsingular transformation groups’, Mem. Fac. Sci. Kyushu Univ. Ser. A 18 (1974), 113133.Google Scholar
[5]Hamachi, T., Oka, Y. and Osikawa, M., ‘Flows associated with ergodic nonsingular transformation groups’, Publ. Res. Inst. Math. Sci. 11 (1975), 3150.CrossRefGoogle Scholar