On close to linear cocycles
Authors:
H. B. Keynes, N. G. Markley and M. Sears
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
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Abstract | References | Similar Articles | Additional Information
Abstract: If we have a flow and a cocycle
on this flow,
, then
is called close to linear if
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
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.
- 1. Hillel Furstenberg, Harvey B. Keynes, Nelson G. Markley, and Michael Sears, Topological properties of 𝑅ⁿ suspensions and growth properties of 𝑍ⁿ cocycles, Proc. London Math. Soc. (3) 66 (1993), no. 2, 431–448. MR 1199074, https://doi.org/10.1112/plms/s3-66.2.431
- 2.
H. B. Keynes, and M. Sears, Time changes for
flows and suspensions, Pacific J Math., 130 No 1 (1987), 97-113.
- 3. H. B. Keynes, N. G. Markley, and M. Sears, On the structure of minimal 𝑅ⁿ actions, Quaestiones Math. 16 (1993), no. 1, 81–102. MR 1217478
- 4. H. B. Keynes, N. G. Markley, and M. Sears, Ergodic averages and integrals of cocycles, Acta Math. Univ. Comemanae LXIV (1995), 123--139.
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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
DOI:
https://doi.org/10.1090/S0002-9939-96-03188-7
Received by editor(s):
February 25, 1994
Received by editor(s) in revised form:
November 11, 1994
Communicated by:
Linda Keen
Article copyright:
© Copyright 1996
American Mathematical Society