Livsic theorems for connected Lie groups
Authors:
M. Pollicott and C. P. Walkden
Journal:
Trans. Amer. Math. Soc. 353 (2001), 28792895
MSC (2000):
Primary 58F11; Secondary 58F15
Published electronically:
March 12, 2001
MathSciNet review:
1828477
Fulltext PDF Free Access
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Abstract: Let be a hyperbolic diffeomorphism on a basic set and let be a connected Lie group. Let be Hölder. Assuming that satisfies a natural partial hyperbolicity assumption, we show that if is a measurable solution to a.e., then must in fact be Hölder. Under an additional centre bunching condition on , we show that if assigns `weight' equal to the identity to each periodic orbit of , then for some Hölder . These results extend wellknown theorems due to Livsic when is compact or abelian.
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 [Hl]
 P. Halmos, Measure theory, Van Nostrand, New York, 1950. MR 11:504d
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 [KH]
 A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Encyclopedia of Math., vol. 54, Cambridge Univ. Press, Cambridge, 1995. MR 96c:58055
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 A. N. Livsic, Homology properties of Ysystems, Math. Notes 10 (1971), 758763.
 [L2]
 A. N. Livsic, Cohomology of dynamical systems, Math. U.S.S.R., Izv. 6 (1972), 12781301.
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 M. Nicol and M. Pollicott, Measurable cocycle rigidity for some noncompact groups, Bull. London. Math. Soc. 31 (1999), 592600. MR 2000k:37004
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 C. P. Walkden, Livsic regularity theorems for twisted cocycle equations over hyperbolic systems, J. London Math. Soc. 61 (2000), 286300. CMP 2000:09
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Additional Information
M. Pollicott
Affiliation:
Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, U.K.
Email:
mp@ma.man.ac.uk
C. P. Walkden
Affiliation:
Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, U.K.
Email:
cwalkden@ma.man.ac.uk
DOI:
http://dx.doi.org/10.1090/S0002994701027088
PII:
S 00029947(01)027088
Received by editor(s):
January 31, 1999
Received by editor(s) in revised form:
April 12, 2000
Published electronically:
March 12, 2001
Article copyright:
© Copyright 2001
American Mathematical Society
