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Smooth $ T\sp n$-valued cocycles for ergodic diffeomorphisms

Author: Jane M. Hawkins
Journal: Proc. Amer. Math. Soc. 93 (1985), 307-311
MSC: Primary 58F11; Secondary 28D99
MathSciNet review: 770542
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Abstract: We prove that if $ f$ is any conservative, ergodic diffeomorphism of a smooth, connected, paracompact manifold, then in the set of smooth $ {T^n}$-valued cocycles on $ X$ for the $ {\mathbf{Z}}$-action determined by $ f$, there is a residual set which give ergodic skew product extensions.

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

  • [H] J. Hawkins, Smooth type III diffeomorphisms of manifolds, Trans. Amer. Math. Soc. 276 (1983), 625-643. MR 688966 (84i:58067)
  • [J] R. Jones and W. Parry, Compact abelian group extensions of dynamical systems. II, Compositio Math. 25 (1972), 135-147. MR 0338318 (49:3083)
  • [K] J. Kelley, General topology, Van Nostrand Reinhold, New York, 1955. MR 0070144 (16:1136c)
  • [S] K. Schmidt, Cocycles on ergodic transformation groups, Macmillan Lectures in Math., Vol. I, Macmillan India, Delhi, 1977. MR 0578731 (58:28262)

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Keywords: Ergodic diffeomorphisms, skew products, smooth cocycles
Article copyright: © Copyright 1985 American Mathematical Society

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