The almost weak specification property for ergodic group automorphisms of abelian groups

Masahito DATEYAMA

doi:10.2969/jmsj/04220341

Masahito DATEYAMA

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JOURNAL FREE ACCESS

1990 Volume 42 Issue 2 Pages 341-351

DOI https://doi.org/10.2969/jmsj/04220341

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Published: 1990 Received: May 02, 1988 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) N. Aoki, A simple proof of Bernoullicity of ergodic automorphisms on compact abelian groups, Israel J. Math., 38 (1981), 189-198.
2) N. Aoki, Zero-dimensional automorphisms with specification, Monatsh. Math., 95 (1983), 1-17.
3) N. Aoki, M. Dateyama and M. Komuro, Solenoidal automorphisms with specifications, Monatsh. Math., 93 (1982), 79-110.
4) M. Dateyama, Invariant measures for homeomorphisms with weak specification, Tokyo J. Math., 4 (1981), 389-397.
5) M. Dateyama, Invariant measures for homeomorphisms with almost weak specification, Lecture Notes in Math., 1021, Springer, 1983, pp. 93-96.
6) M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math., 527, Springer, 1976.
7) B. Marcus, A note on periodic points for ergodic toral automorphisms, Monatsh. Math., 89 (1980), 121-129.
8) J. Miles and K. Thomas, Generalized torus are Bernoulli, Studies in Ergodic Theory and Probability, vol. 2, Academic Press, New York, 1978, pp. 231-249.
9) L. Pontrjagin, Topological Groups, Gordon & Breach, New York-London-Paris, 1966.
10) K. Sigmund, Generic properties of invariant measures for axiom A diffeomorphisms, Invent. Math., 11 (1970), 99-109.
11) K. Sigmund, On dynamical systems with the specification property, Trans. Amer. Math. Soc., 190 (1974), 285-299.

Right : [1] N. Aoki, A simple proof of Bernoullicity of ergodic automorphisms on compact abelian groups, Israel J. Math., 38 (1981), 189-198.
[2] N. Aoki, Zero-dimensional automorphisms with specification, Monatsh. Math., 95 (1983), 1-17.
[3] N. Aoki, M. Dateyama and M. Komuro, Solenoidal automorphisms with specifications, Monatsh. Math., 93 (1982), 79-110.
[4] M. Dateyama, Invariant measures for homeomorphisms with weak specification, Tokyo J. Math., 4 (1981), 389-397.
[5] M. Dateyama, Invariant measures for homeomorphisms with almost weak specification, Lecture Notes in Math., 1021, Springer, 1983, pp. 93-96.
[6] M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces, Lecture Notes in Math., 527, Springer, 1976.
[7] B. Marcus, A note on periodic points for ergodic toral automorphisms, Monatsh. Math., 89 (1980), 121-129.
[8] J. Miles and K. Thomas, Generalized torus are Bernoulli, Studies in Ergodic Theory and Probability, vol. 2, Academic Press, New York, 1978, pp. 231-249.
[9] L. Pontrjagin, Topological Groups, Gordon & Breach, New York-London-Paris, 1966.
[10] K. Sigmund, Generic properties of invariant measures for axiom A diffeomorphisms, Invent. Math., 11 (1970), 99-109.
[11] K. Sigmund, On dynamical systems with the specification property, Trans. Amer. Math. Soc., 190 (1974), 285-299.

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