Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The addition theorem for the entropy of transformations of $ G$-spaces


Author: R. K. Thomas
Journal: Trans. Amer. Math. Soc. 160 (1971), 119-130
MSC: Primary 28A65
DOI: https://doi.org/10.1090/S0002-9947-1971-0293064-6
MathSciNet review: 0293064
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For a measure-preserving transformation $ T$ which is a skew-product of a measure-preserving transformation $ S$ and a topological group endomorphism $ \sigma $, it is shown that the entropy $ h$ satisfies the following ``addition theorem": $ h(T) = h(S) + h(\sigma )$.


References [Enhancements On Off] (What's this?)

  • [1] L. M. Abramov and V. A. Rohlin, The entropy of skew product measure-preserving transformations, Vestnik Leningrad. Univ. 17 (1962), 5-13; English transl., Amer. Math. Soc. Transl. (2) 48 (1965), 255-265. MR 25 #4076. MR 0140660 (25:4076)
  • [2] S. A. Juzvinskiĭ, Metric properties of endomorphisms of compact groups, Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965), 1295-1328; English transl., Amer. Math. Soc. Transl. (2) 66 (1968), 63-98. MR 33 #2798. MR 0194588 (33:2798)
  • [3] V. A. Rohlin, Lectures on the entropy theory of measure preserving transformations with invariant measure, Uspehi Mat. Nauk 22 (1967), no. 5 (137), 3-56 = Russian Math. Surveys 22 (1967), no. 5, 1-52. MR 36 #349. MR 0217258 (36:349)
  • [4] R. K. Thomas, Metric properties of transformations of $ G$-spaces, Trans. Amer. Math. Soc. 60 (1971), 103-117. MR 0293063 (45:2142)
  • [5] S. Helgason, Differential geometry and symmetric spaces, Pure and Appl. Math., vol. 12, Academic Press, New York, 1962. MR 26 #2986. MR 0145455 (26:2986)
  • [6] V. A. Rohlin, Metric properties of endomorphisms of compact commutative groups, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 867-874; English transl., Amer. Math. Soc. Transl. (2) 64 (1967), 244-252. MR 29 #5955. MR 0168697 (29:5955)
  • [7] W. Parry, Ergodic properties of affine transformations and flows on nilmanifolds, Amer. J. Math. 91 (1969), 757-771. MR 0260975 (41:5595)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 28A65

Retrieve articles in all journals with MSC: 28A65


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0293064-6
Keywords: Skew-product transformation, addition theorem, rigid groups
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society