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Poorly Approximated ℤ2-Cocycles For Transformations With Rational Discrete Spectrum

Published online by Cambridge University Press:  20 November 2018

Adam Fieldsteel
Adam Fieldsteel*
Affiliation:
Department of Mathematics, Wesley an University, Middletown, CT, USA 06459
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Abstract

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Let T be an ergodic automorphism with rational discrete spectrum and ϕ a ℤ2-cocyle for T. We show that the resulting two-point extension of T is cohomologous to a Morse cocycle if ϕ is approximated with speed o(1/n).

On the other hand, we show by example that this is in general false when the speed of approximation is O(1/n).

Keywords

28D05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 3 , 01 September 1991 , pp. 338 - 342
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Filipowicz, I., Kwiatkowski, J. and Lemanczyk, M., Approximation Z2-cocycles and shift dynamical systems , Publ. Mat. 32(1988),91–110.Google Scholar
2. Keane, M., Generalized Morse sequences, Z. Wahr. Verw. Geb. 10 (1968), 335–353.Google Scholar