Geodesic
The affine connection in the normal coordinates
Matematičeskie trudy, Tome 15 (2012) no. 1, pp. 27-54

Voir la notice de l'article provenant de la source Math-Net.Ru

We propose a method to calculate the derivatives of the Christoffel symbols in the normal coordinates on a smooth manifold with symmetric affine connection. As an application, we construct an algorithm for computing the Taylor series of the double exponential map. 
@article{MT_2012_15_1_a1,
     author = {A. V. Gavrilov},
     title = {The affine connection in the normal coordinates},
     journal = {Matemati\v{c}eskie trudy},
     pages = {27--54},
     publisher = {mathdoc},
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     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2012_15_1_a1/}
}
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A. V. Gavrilov. The affine connection in the normal coordinates. Matematičeskie trudy, Tome 15 (2012) no. 1, pp. 27-54. http://geodesic.mathdoc.fr/item/MT_2012_15_1_a1/