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Regularity results for the solutions of the Livsic cohomology equation with values in diffeomorphism groups

Published online by Cambridge University Press:  19 September 2008

Viorel Niţcă  and
Andrei Török
Viorel Niţcă
Affiliation:
Institute of Mathematics of the Romanian Academy, PO Box 1–764, RO-70700 Bucharest, Romania
Andrei Török
Affiliation:
Institute of Mathematics of the Romanian Academy, PO Box 1–764, RO-70700 Bucharest, Romania
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Abstract

In this paper we obtain regularity results for the Livsic cohomology equation for cocycles with values in diffeomorphism groups and Lie groups.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 2 , April 1996 , pp. 325 - 333
Copyright
Copyright © Cambridge University Press 1996

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References

REFERENCES

[C-E-G]Collet, P., Epstein, H. and Gallavoti, G.. Perturbations of geodesic flows on surfaces of constant negative curvature and their mixing properties. Commun. Math. Phys. 95 (1984), 61–112.CrossRefGoogle Scholar
[G-K1]Guillemin, V. and Kazhdan, D.. On the cohomology of certain dynamical systems. Topology 19 (1980), 291–299.CrossRefGoogle Scholar
[G-K2]Guillemin, V. and Kazhdan, D.. Some inverse spectral results for negatively curved 2-manifolds. Topology 19 (1980), 301–313.CrossRefGoogle Scholar
[H-P-S]Hirsch, M., Pugh, C. and Shub, M.. Invariant Manifolds. Springer Lecture Notes in Mathematics 583. Springer, Berlin, 1977.CrossRefGoogle Scholar
[J]Journé, J.-L.. A regularity lemma for functions of several variables. Revista Matematica Iberoamericana 4(2) (1988), 187–193.CrossRefGoogle Scholar
[K-H]Katok, A. and Hurder, S.. Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Publ. Math. Inst. Hautes Etudes Sci. 72 (1990), 5–61.Google Scholar
[L1]Livsic, A.. Homology properties of U systems. Math. Notes 10 (1971), 758–763.Google Scholar
[L2]Livsic, A.. Cohomology of dynamical systems. Math. U.S.S.R., Izvestia 6 (1972), 1278–1301.Google Scholar
[L]Llave, R. de la. Analytic regularity of solutions of Livsic's cohomology equations and some applications to analytic conjugacy of hyperbolic dynamical systems. Preprint. (1989).Google Scholar
[L-M-M]Llave, R. de la, Marco, J. M. and Moryion, R.. Canonical perturbation theory of Anosov systems and regularity results for Livsic cohomology equation. Ann. Math. 123 (1986), 537–612.CrossRefGoogle Scholar
[N-T]Niţicà, V and Török, A.. Cohomology of dynamical systems and rigidity of partially hyperbolic actions of higher rank lattices. Duke Math. J. 79 (1995), 751–810.CrossRefGoogle Scholar
[Sm]Smale, S.. Differentiable dynamical systems. Bull. Amer. Math. Soc. 73 (1967), 747–817.CrossRefGoogle Scholar
[Sh]Shub, M.. Stabilité globale des systemes dynamiques. Asterisque 56 (1978), 1–211.Google Scholar