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Continuous invariant cone families and ergodicity of flows in dimension three

Published online by Cambridge University Press:  19 September 2008

Keith Burns  and
Marlies Gerber
Keith Burns
Affiliation:
Department of mathematics, Indiana university, Bloomington, IN 47405, USA
Marlies Gerber
Affiliation:
Department of mathematics, Indiana university, Bloomington, IN 47405, USA
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Abstract

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It is shown that a C2 flow on a compact three-dimensional manifold that preserves a smooth measure and has a continuous family of cones satisfying a certain invariance property must be ergodic.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 1 , March 1989 , pp. 19 - 25
Copyright
Copyright © Cambridge University Press 1989

References

REFERENCES

[BG1]Burns, K. & Gerber, M.. Bernoulli geodesic flows on S 2. Preprint, 1987.Google Scholar
[BG2]Burns, K. & Gerber, M.. Real analytic Bernoulli geodesic flows on S 2. Preprint, 1987. To appear in Ergod. Th. & Dynatn. Sys.Google Scholar
[D1]Donnay, V. J.. Geodesic flow on S 2 with positive measure entropy. Preprint, 1986.Google Scholar
[D2]Donnay, V. J.. Geodesic flow on the two-sphere with positive entropy. Thesis, Ph.D., New YorkUniversity,1986.Google Scholar
[D3]Donnay, V. J.. Geodesic flow on the two-sphere, Part I: Positive measure entropy. Preprint, 1987.CrossRefGoogle Scholar
[D4]Donnay, V. J.. Geodesic flow on the two-sphere, Part II: Ergodicity. Preprint, 1987.CrossRefGoogle Scholar
[FHY]Fathi, A., Herman, M. R., Yoccoz, J. C.. A proof of Pesin's stable manifold theorem. Lecture Notes in Mathematics 1007, pp. 177–215. Springer: New York, 1983.Google Scholar
[K]Katok, A.. Invariant cone families and stochastic properties of smooth dynamical systems. Preprint, 1987.Google Scholar
[O]Osceledec, V. I.. A multiplicative ergodic theorem: characteristic Lyapunov exponents of dynamical systems. Trans. Moscow Math. Soc. 19 (1968), 197–231.Google Scholar
[P]Pesin, Ya. B.. Characteristic Lyapunov exponents and smooth ergodic theory. Russian Math. Surveys 32 (1977), 55–114.CrossRefGoogle Scholar
[W]Wojtkowski, M.. Invariant families of cones and Lyapunov exponents. Ergod. Th. & Dynam. Sys. 5 (1985), 145–161.CrossRefGoogle Scholar