Residuality of dynamical morphisms

R. Burton; M. Keane; Jacek Serafin

Colloquium Mathematicae (2000)

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

Abstract

top
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.

How to cite

top

Burton, 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. [1] P. Billingsley, Ergodic Theory and Information, Wiley, New York, 1965. Zbl0141.16702
  2. [2] R. Burton and A. Rothstein, Isomorphism theorems in ergodic theory, Technical Report, Oregon State Univ., 1977. 
  3. [3] H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton Univ. Press, Princeton, NJ, 1981. Zbl0459.28023
  4. [4] P. Halmos and H. Vaughan, The Marriage Problem, Amer. J. Math.72 (1950), 214-215. Zbl0034.29601
  5. [5] K. Jacobs, Lecture Notes on Ergodic Theory, Aarhus Univ., 1962. 
  6. [6] J. Kammeyer, The isomorphism theorem for relatively finitely determined ℤ n -actions, Israel J. Math.69 (1990), 117-127. Zbl0699.28009
  7. [7] M. Keane and J. Serafin, On the countable generator theorem, Fund. Math.157 (1998), 255-259. Zbl0915.28008
  8. [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. [9] W. Krieger, On entropy and generators of measure-% preserving transformations, Trans. Amer. Math. Soc.149 (1970), 453-464. Zbl0204.07904
  10. [10] V. A. Rokhlin, Lectures on the entropy theory of measure-preserving transformations, Russian Math. Surveys22 (1967), no. 5, 1-52. Zbl0174.45501
  11. [11] D. Ornstein, Bernoulli shifts with the same entropy are isomorphic, Adv. Math.4 (1970), 337-352. Zbl0197.33502
  12. [12] D. Ornstein, Ergodic Theory, Randomness and Dynamical Systems, Yale Univ. Press, New Haven, 1974. Zbl0296.28016
  13. [13] J. Serafin, Finitary codes and isomorphisms, Ph.D. Thesis, Technische Universiteit Delft, 1996. 
  14. [14] Ya. Sinai, A weak isomorphism of transformations with an invariant measure, Dokl. Akad. Nauk SSSR 147 (1962), 797-800 (in Russian). 
  15. [15] P. Walters, An Introduction to Ergodic Theory, Springer, 1982. Zbl0475.28009

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.