Geodesic
Jacobi Fields along a Geodesic with Random Curvature
Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 416-424

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A notion of a renewable geodesic on which the curvature is a random process is introduced. It is shown that the modulus of the Jacobi field along such a geodesic grows exponentially. At the same time, the existence with probability 1 of infinitely many conjugate points is demonstrated. 
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     author = {V. G. Lamburt and D. D. Sokolov and V. N. Tutubalin},
     title = {Jacobi {Fields} along a {Geodesic} with {Random} {Curvature}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {416--424},
     publisher = {mathdoc},
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     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a9/}
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V. G. Lamburt; D. D. Sokolov; V. N. Tutubalin. Jacobi Fields along a Geodesic with Random Curvature. Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 416-424. http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a9/