Markov subshifts and realization of β-expansions

Shunji ITO; Yoichiro TAKAHASHI

doi:10.2969/jmsj/02610033

Shunji ITO, Yoichiro TAKAHASHI

Author information

JOURNAL FREE ACCESS

1974 Volume 26 Issue 1 Pages 33-55

DOI https://doi.org/10.2969/jmsj/02610033

Details

Published: 1974 Received: June 20, 1972 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: September 29, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Shunji ITO¹⁾, Yoichiro TAKAHASHI²⁾
Right : Shunji ITO¹⁾, Yoichiro TAKAHASHI²⁾³⁾

Date of correction: September 29, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Department of the Foundations of Mathematical Sciences Tokyo University of Education
2) Department of Mathematics Hiroshima University

Right :
1) Department of the Foundations of Mathematical Sciences Tokyo University of Education
2) Department of Mathematics Hiroshima University
3) Department of Mathematics College of General Education University of Tokyo

Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. L. Adler and B. Weiss, Similarity of automorphisms of the torus, Memoires of the Amer. Math. Soc., No. 98.
2) M. Artin and B. Mazur, On periodic points, Ann, of Math., 81 (1965), 82-99.
3) R. Bowen, Markov partitions for Axiom A diffeomorphisms, Amer. J. Math., 92 (1970), 725-747.
4) R. Bowen, Periodic points and measures for Axiom A diffeomorphisms, Trans. Amer. Math. Soc., 154 (1971), 377-397.
5) F. R. Gantmacher, Theory of matrices, Part II, New York, 1960, (English translation).
6) G. A. Hedlund, Transformations commuting with the shift, in “Topological dynamics”, (Auslander and Gottchalk ed), 1968, 259-289.
7) N. Iwahori, On stochastic matrices of a given Frobenius type, J. Fac. Sci. Univ. Tokyo Sect. I, 13 (1966), 139-161.
8) H. B. Keynes and J. B. Robertson, Generators for topological entropy and expansiveness, Math. Systems Theory, 3 (1969), 51-59.
9) K. R. Meyer, Periodic points of diffeomorphisms, Bull. Amer. Math. Soc., 73 (1967), 615-617.
10) W. Parry, On the β-expansions of real numbers, Acta Math. Acad. Sci. Hungar., 11 (1960), 401-416.
11) W. Parry, Intrinsic Markov chains, Trans. Amer. Math. Soc., 112 (1964), 55-66.
12) A. Renyi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar., 8 (1957), 447-493.
13) Ya. G. Sinai, Markov partitions and C-diffeomorphisms, Funkcional. Anal. i Prilozen, 2, No. 1 (1968), 64-89.
14) S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 747-817.
15) Smorodinsky, β-automorphisms are Bernoulli shifts, (preprint).
16) Y. Takahashi, Isomorphisms of β-automorphisms to Markov automorphisms, Osaka Math. J.

Right : [1] R. L. Adler and B. Weiss, Similarity of automorphisms of the torus, Memoires of the Amer. Math. Soc., No. 98.
[2] M. Artin and B. Mazur, On periodic points, Ann, of Math., 81 (1965), 82-99.
[3] R. Bowen, Markov partitions for Axiom A diffeomorphisms, Amer. J. Math., 92 (1970), 725-747.
[4] R. Bowen, Periodic points and measures for Axiom A diffeomorphisms, Trans. Amer. Math. Soc., 154 (1971), 377-397.
[5] F. R. Gantmacher, Theory of matrices, Part II, New York, 1960, (English translation).
[6] G. A. Hedlund, Transformations commuting with the shift, in “Topological dynamics”, (Auslander and Gottchalk ed), 1968, 259-289.
[7] N. Iwahori, On stochastic matrices of a given Frobenius type, J. Fac. Sci. Univ. Tokyo Sect. I, 13 (1966), 139-161.
[8] H. B. Keynes and J. B. Robertson, Generators for topological entropy and expansiveness, Math. Systems Theory, 3 (1969), 51-59.
[9] K. R. Meyer, Periodic points of diffeomorphisms, Bull. Amer. Math. Soc., 73 (1967), 615-617.
[10] W. Parry, On the β-expansions of real numbers, Acta Math. Acad. Sci. Hungar., 11 (1960), 401-416.
[11] W. Parry, Intrinsic Markov chains, Trans. Amer. Math. Soc., 112 (1964), 55-66.
[12] A. Renyi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar., 8 (1957), 447-493.
[13] Ya. G. Sinai, Markov partitions and C-diffeomorphisms, Funkcional. Anal. i Prilozen, 2, No. 1 (1968), 64-89.
[14] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 747-817.
[15] Smorodinsky, β-automorphisms are Bernoulli shifts, (preprint).
[16] Y. Takahashi, Isomorphisms of β-automorphisms to Markov automorphisms, Osaka Math. J.

Date of correction: September 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

Corresponding author

Correction information

Register with J-STAGE for free!