# Residuality of dynamical morphisms

R. Burton; M. Keane; Jacek Serafin

Colloquium Mathematicae (2000)

- Volume: 84/85, Issue: 2, page 307-317
- ISSN: 0010-1354

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topBurton, R., Keane, M., and Serafin, Jacek. "Residuality of dynamical morphisms." Colloquium Mathematicae 84/85.2 (2000): 307-317. <http://eudml.org/doc/210815>.

@article{Burton2000,

abstract = {We present a unified approach to the finite generator theorem of Krieger, the homomorphism theorem of Sinai and the isomorphism theorem of Ornstein. We show that in a suitable space of measures those measures which define isomorphisms or respectively homomorphisms form residual subsets.},

author = {Burton, R., Keane, M., Serafin, Jacek},

journal = {Colloquium Mathematicae},

keywords = {entropy; finite generator theorem; isomorphism of Bernoulli shifts},

language = {eng},

number = {2},

pages = {307-317},

title = {Residuality of dynamical morphisms},

url = {http://eudml.org/doc/210815},

volume = {84/85},

year = {2000},

}

TY - JOUR

AU - Burton, R.

AU - Keane, M.

AU - Serafin, Jacek

TI - Residuality of dynamical morphisms

JO - Colloquium Mathematicae

PY - 2000

VL - 84/85

IS - 2

SP - 307

EP - 317

AB - We present a unified approach to the finite generator theorem of Krieger, the homomorphism theorem of Sinai and the isomorphism theorem of Ornstein. We show that in a suitable space of measures those measures which define isomorphisms or respectively homomorphisms form residual subsets.

LA - eng

KW - entropy; finite generator theorem; isomorphism of Bernoulli shifts

UR - http://eudml.org/doc/210815

ER -

## References

top- [1] P. Billingsley, Ergodic Theory and Information, Wiley, New York, 1965. Zbl0141.16702
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- [7] M. Keane and J. Serafin, On the countable generator theorem, Fund. Math.157 (1998), 255-259. Zbl0915.28008
- [8] M. Keane and M. Smorodinsky, Bernoulli schemes of the same entropy are finitarily isomorphic, Ann. of Math.109 (1979), 397-406. Zbl0405.28017
- [9] W. Krieger, On entropy and generators of measure-% preserving transformations, Trans. Amer. Math. Soc.149 (1970), 453-464. Zbl0204.07904
- [10] V. A. Rokhlin, Lectures on the entropy theory of measure-preserving transformations, Russian Math. Surveys22 (1967), no. 5, 1-52. Zbl0174.45501
- [11] D. Ornstein, Bernoulli shifts with the same entropy are isomorphic, Adv. Math.4 (1970), 337-352. Zbl0197.33502
- [12] D. Ornstein, Ergodic Theory, Randomness and Dynamical Systems, Yale Univ. Press, New Haven, 1974. Zbl0296.28016
- [13] J. Serafin, Finitary codes and isomorphisms, Ph.D. Thesis, Technische Universiteit Delft, 1996.
- [14] Ya. Sinai, A weak isomorphism of transformations with an invariant measure, Dokl. Akad. Nauk SSSR 147 (1962), 797-800 (in Russian).
- [15] P. Walters, An Introduction to Ergodic Theory, Springer, 1982. Zbl0475.28009

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