Skew-products with simple approximations

Author:
P. N. Whitman

Journal:
Proc. Amer. Math. Soc. **72** (1978), 521-526

MSC:
Primary 28D05

DOI:
https://doi.org/10.1090/S0002-9939-1978-0509247-5

MathSciNet review:
509247

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Abstract: Conditions are given in order that the cartesian product of two measure-preserving invertible transformations admits an approximation. A class of skew-product transformations is defined and conditions are given for a member of this class to admit a simple approximation.

**[1]**R. V. Chacon,*Approximations and spectral multiplicity*, Lecture Notes in Math., vol. 160, Springer-Verlag, Berlin and New York, 1970, pp. 18-27. MR**42**#6186. MR**0271303 (42:6186)****[2]**G. R. Goodson,*Skew-products with simple spectrum*, J. London Math. Soc. (2)**10**(1975), 441-446. MR**52**#703. MR**0379798 (52:703)****[3]**F. Hahn and W. Parry,*Some characteristic properties of dynamical systems with quasi-discrete spectrum*, Math Systems Theory**2**(1968), 179-190. MR**37**#6435. MR**0230877 (37:6435)****[4]**A. B. Katok and A. M. Stepin,*Approximations in ergodic theory*, Russian Math. Surveys (5)**22**(1967), 77-102. MR**36**#2776. MR**0219697 (36:2776)****[5]**D. Newton,*On the entropy of certain classes of skew-product transformations*, Proc. Amer. Math. Soc.**21**(1969), 722-726. MR**40**# 1581. MR**0248329 (40:1581)****[6]**P. N. Whitman,*Approximation of induced automorphisms and special automorphisms*, Proc. Amer. Math. Soc.**70**(1978), 139-145. MR**0486429 (58:6175)**

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DOI:
https://doi.org/10.1090/S0002-9939-1978-0509247-5

Article copyright:
© Copyright 1978
American Mathematical Society