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Equations for the entropy of a geodesic flow on a compact Riemannian manifold without conjugate points. (English) Zbl 0411.58016


MSC:

37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
28D20 Entropy and other invariants
53C20 Global Riemannian geometry, including pinching
53C22 Geodesics in global differential geometry
37A99 Ergodic theory

Citations:

Zbl 0399.58009
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Full Text: DOI

References:

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[9] W. Klingenberg, ?Riemannian manifolds with geodesic flow of Anosov type,? Ann. Math.,99, 1-13 (1974). · Zbl 0272.53025 · doi:10.2307/1971011
[10] P. Eberlein, ?Geodesic flows on negatively curved manifolds. I,? Ann. Math.,95, 492-510 (1972). · Zbl 0217.47304 · doi:10.2307/1970869
[11] E. Heinfze and H.-C. Im Hof, ?On the geometry of horospheres,? Preprint, Bonn (1975).
[12] J. H. Eschenburg, ?Horospheres and the stable part of the geodesic flow,? Math. Z.,1953, 237-251 (1977). · Zbl 0338.53029 · doi:10.1007/BF01214477
[13] L. W. Green, ?A theorem of E. Hopf,? Michigan Math. J.,5, 31-34 (1958). · Zbl 0134.39601 · doi:10.1307/mmj/1028998009
[14] V. I. Arnold, Ordinary Differential Equations, MIT Press (1973). · Zbl 0296.34001
[15] Ya. B. Pesin, ?Families of invariant manifolds, corresponding to nonzero characteristic exponents,? Izv. Akad. Nauk SSSR, Ser. Mat.,40, No. 6, 1332-1379 (1976).
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