Geodesic
The existence of convex spherical metrics, all closed nonselfintersecting geodesics of which are hyperbolic
Izvestiya. Mathematics , Tome 14 (1980) no. 1, pp. 1-16.

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In this paper it is shown that in any $C^1$-neighborhood of the standard metric $H_0$ on $S^2$, there exists a subset consisting of convex metrics, which is open in the $C^2$-topology, and all of whose closed nonselfintersecting geodesics are hyperbolic. Bibliography: 13 titles. 
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A. I. Gryuntal'. The existence of convex spherical metrics, all closed nonselfintersecting geodesics of which are hyperbolic. Izvestiya. Mathematics , Tome 14 (1980) no. 1, pp. 1-16. http://geodesic.mathdoc.fr/item/IM2_1980_14_1_a0/

[1] Puankare A., Izbrannye trudy, t. 2, Nauka, M., 1972

[2] Lyusternik L. A., Shnirelman L. G., Topologicheskie metody v variatsionnykh zadachakh, Issledovatelskii institut matematiki i mekhaniki, M., 1930

[3] Morse M., The calculas of variations in the large, N.Y., 1934

[4] Gryuntal A. I., “Suschestvovanie zamknutoi samoneperesekayuscheisya geodezicheskoi obschego ellipticheskogo tipa na poverkhnostyakh, blizkikh k sfere”, Matem. zametki, 24:2 (1978), 267–278 | MR | Zbl

[5] Gryuntal A. I., “Suschestvovanie metrik na dvumernoi sfere, vse zamknutye samoneperesekayuschiesya geodezicheskie kotorykh giperbolicheskie”, Zasedaniya Moskovskogo matematicheskogo obschestva, Uspekhi matem. nauk, 32:5 (1977), 166

[6] Irwin M. C., “On the smoothness of the composition map”, The Quarterly Journal of Mathematics, Oxford second series, 23:90 (1972), 113–135 | DOI | MR

[7] Godbiion K., Differentsialnaya geometriya i analiticheskaya mekhanika, Mir, M., 1973

[8] Nitetski Z., Vvedenie v differentsialnuyu dinamiku, Mir, M., 1975 | MR | Zbl

[9] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR | Zbl

[10] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR

[11] Kartan A., Differentsialnoe ischislenie. Differentsialnye formy, Mir, M., 1971 | MR | Zbl

[12] Petrovskii I. G., Lektsii po teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1970 | MR

[13] Zigel K. L., Lektsii po nebesnoi mekhanike, IL, M., 1959