## A geometric criterion for hyperbolicity of flows.(English)Zbl 0316.58015

### MSC:

 37D99 Dynamical systems with hyperbolic behavior 28D05 Measure-preserving transformations 53C20 Global Riemannian geometry, including pinching
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### References:

 [1] D. V. Anosov, Geodesic flows on closed Riemannian manifolds of negative curvature, Trudy Mat. Inst. Steklov. 90 (1967), 209 (Russian). · Zbl 0163.43604 [2] M. F. Atiyah, \?-theory, Lecture notes by D. W. Anderson, W. A. Benjamin, Inc., New York-Amsterdam, 1967. [3] D. L. Rod, G. Pecelli, and R. C. Churchill, Hyperbolic periodic orbits, J. Differential Equations 24 (1977), no. 3, 329 – 348. · Zbl 0313.34043 [4] C. C. Conley, The gradient structure of a flow: I, IBM Research, RC 3932 (#17806), Yorktown Heights, New York, July 17, 1972. · Zbl 0309.34041 [5] J. J. Duistermaat, Fourier integral operators, Courant Institute of Mathematical Sciences, New York University, New York, 1973. Translated from Dutch notes of a course given at Nijmegen University, February 1970 to December 1971. · Zbl 0272.47028 [6] Patrick Eberlein, When is a geodesic flow of Anosov type? I,II, J. Differential Geometry 8 (1973), 437 – 463; ibid. 8 (1973), 565 – 577. · Zbl 0285.58008 [7] John E. Franke and James F. Selgrade, Hyperbolicity and chain recurrence, J. Differential Equations 26 (1977), no. 1, 27 – 36. · Zbl 0329.58012 [8] -, Abstract $$\omega$$-limit sets, chain recurrent sets, and basic sets for flows, Proc. Amer. Math. Soc. (to appear). · Zbl 0316.58014 [9] Wilhelm Klingenberg, Riemannian manifolds with geodesic flow of Anosov type, Ann. of Math. (2) 99 (1974), 1 – 13. · Zbl 0272.53025 [10] Ricardo Mañé, Persitent manifolds are normally hyperbolic, Bull. Amer. Math. Soc. 80 (1974), 90 – 91. · Zbl 0276.58009 [11] J. Milnor, Morse theory, Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. · Zbl 0108.10401 [12] Robert J. Sacker and George R. Sell, Existence of dichotomies and invariant splittings for linear differential systems. I, J. Differential Equations 15 (1974), 429 – 458. · Zbl 0294.58008 [13] James F. Selgrade, Isolated invariant sets for flows on vector bundles, Trans. Amer. Math. Soc. 203 (1975), 359 – 390. · Zbl 0265.58004
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