On close to linear cocycles
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- by H. B. Keynes, N. G. Markley and M. Sears PDF
- Proc. Amer. Math. Soc. 124 (1996), 1923-1931 Request permission
Abstract:
If we have a flow $(X,\Bbb {Z}^m)$ and a cocycle $h$ on this flow, $h:X\times \Bbb {Z}^m\rightarrow \Bbb {R}^m$, then $h$ is called close to linear if $h$ can be written as the direct sum of a linear (constant) cocycle and a cocycle in the closure of the coboundaries. Many of the desirable consequences of linearity hold for such cocycles and, in fact, a close to linear cocycle is cohomologous to a cocycle which is norm close to a linear one. Furthermore in the uniquely ergodic case all cocycles are close to linear. We also establish that a close to linear cocycle which is covering is cohomologous to one with the special property that it can be extended by piecewise linearity to an invertible cocycle from $X\times \Bbb {R}^m$ to itself. This implies that a suspension obtained from a close to linear cocycle is isomorphic to a time change of the suspension obtained from the identity cocycle.References
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- H. B. Keynes, and M. Sears, Time changes for $\Bbb {R}^n$ flows and suspensions, Pacific J Math., 130 No 1 (1987), 97-113.
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- H. B. Keynes, N. G. Markley, and M. Sears, Ergodic averages and integrals of cocycles, Acta Math. Univ. Comemanae LXIV (1995), 123–139.
Additional Information
- H. B. Keynes
- Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- Email: keynes@math.umn.edu
- N. G. Markley
- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- Email: ngm@glve.umd.edu
- M. Sears
- Affiliation: Department of Mathematics, University of the Witwatersrand, Johannesburg, South Africa
- Email: 036mis@cosmos.wits.ac.za
- Received by editor(s): February 25, 1994
- Received by editor(s) in revised form: November 11, 1994
- Communicated by: Linda Keen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1923-1931
- MSC (1991): Primary 58F25; Secondary 28D10, 54H20
- DOI: https://doi.org/10.1090/S0002-9939-96-03188-7
- MathSciNet review: 1307537