Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the ergodicity of a class of real skew product extensions of approximations


Author: G. R. Goodson
Journal: Proc. Amer. Math. Soc. 86 (1982), 417-422
MSC: Primary 28D99
DOI: https://doi.org/10.1090/S0002-9939-1982-0671207-2
MathSciNet review: 671207
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper conditions are given for real skew product extensions of cyclic $ KS$ approximations to be ergodic. These results are then applied to show that if $ {T_\alpha }$ is an irrational rotation on the unit circle, there exists an uncountable dense collection of measurable sets for which the corresponding skew product extension is ergodic.


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

  • [1] G. Atkinson and G. W. Riley, On the ergodicity of some real line extensions of irrational rotations, Preprint, Univ. of Warwick, 1978.
  • [2] G. H. Hardy and J. E. Littlewood, Some problems of Diophantine approximation, Acta Math. 37 (1914), 155-191. MR 1555098
  • [3] A. B. Katok and A. M. Stepin, Approximations in ergodic theory, Russian Math. Surveys 22 (1967), 77-102. MR 0219697 (36:2776)
  • [4] K. Schmidt, Lectures on cocycles of ergodic transformation groups, Preprint, Univ. of Warwick, 1976. MR 0578731 (58:28262)
  • [5] H. Weyl, Über die Gleichverteilung von Zahlen mod Eins, Math. Ann. 77 (1916), 313-352. MR 1511862

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28D99

Retrieve articles in all journals with MSC: 28D99


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0671207-2
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society