no. 4
Conjugate and Cut Loci of a Two-Sphere of Revolution With Application to Optimal Control
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1081-1098. 
@article{AIHPC_2009__26_4_1081_0,
     author = {Bonnard, Bernard and Caillau, Jean-Baptiste and Sinclair, Robert and Tanaka, Minoru},
     title = {Conjugate and {Cut} {Loci} of a {Two-Sphere} of {Revolution} {With} {Application} to {Optimal} {Control}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1081--1098},
     publisher = {Elsevier},
     volume = {26},
     number = {4},
     year = {2009},
     doi = {10.1016/j.anihpc.2008.03.010},
     mrnumber = {2542715},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2008.03.010/}
}
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Bonnard, Bernard; Caillau, Jean-Baptiste; Sinclair, Robert; Tanaka, Minoru. Conjugate and Cut Loci of a Two-Sphere of Revolution With Application to Optimal Control. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1081-1098. doi : 10.1016/j.anihpc.2008.03.010. http://archive.numdam.org/articles/10.1016/j.anihpc.2008.03.010/

[1] A. Agrachev, U. Boscain, M. Sigalotti, A Gauss-Bonnet like formula on two-dimensional almost Riemannian manifolds, Preprint SISSA 55/2006/M, 2006. | MR

[2] Bao D., Robles C., Shen Z., Zermelo Navigation on Riemannian Manifolds, J. Differential Geom. 66 (3) (2004) 377-435. | MR | Zbl

[3] Berger M., A Panoramic View of Riemannian Geometry, Springer-Verlag, Berlin, 2003. | MR | Zbl

[4] Bonnard B., Caillau J.-B., Optimality Results in Orbit Transfer, C. R. Acad. Sci. Paris, Ser. I 345 (2007) 319-324. | MR | Zbl

[5] Bonnard B., Caillau J.-B., Dujol R., Energy Minimization of Single-Input Orbit Transfer by Averaging and Continuation, Bull. Sci. Math. 130 (8) (2006) 707-719. | MR | Zbl

[6] Bonnard B., Caillau J.-B., Riemannian Metric of the Averaged Energy Minimization Problem in Orbital Transfer With Low Thrust, Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (3) (2007) 395-411. | Numdam | MR | Zbl

[7] B. Bonnard, D. Sugny, Optimal control with applications in space and quantum dynamics, Preprint Institut math. Bourgogne, 2007.

[8] B. Bonnard, J.B. Caillau, M. Tanaka, One-parameter family of Clairaut-Liouville metrics with application to optimal control, HAL preprint No 00177686 (2007), url: hal.archives-ouvertes.fr/hal-00177686.

[9] Bonnard B., Chyba M., Singular Trajectories and Their Role in Control Theory, Springer-Verlag, Berlin, 2003. | MR | Zbl

[10] Gluck H., Singer D., Scattering of Geodesic Fields I and II, Ann. of Math. 108 (1978) 347-372, and 110 (1979) 205-225. | MR | Zbl

[11] Gravesen J., Markvorsen S., Sinclair R., Tanaka M., The Cut Locus of a Torus of Revolution, Asian J. Math. 9 (2005) 103-120. | MR | Zbl

[12] Hebda J. J., Metric Structure of Cut Loci in Surfaces and Ambrose's Problem, J. Differential Geom. 40 (1994) 621-642. | MR | Zbl

[13] Itoh J. I., Kiyohara K., The Cut Loci and the Conjugate Loci on Ellipsoids, Manuscripta Math. 114 (2004) 247-264. | MR | Zbl

[14] K. Fleischmann, Die geodätischen Linien auf Rotationsflächen, Liegnitz, Dissertation, Seyffarth, 1915. Persistent URL: http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN317487884. | JFM

[15] Myers S. B., Connections Between Differential Geometry and Topology: I. Simply Connected Surfaces and II. Closed Surfaces, Duke Math. J. 1 (1935) 376-391, and 2 (1936) 95-102. | JFM | MR

[16] Poincaré H., Sur Les Lignes Géodésiques Des Surfaces Convexes, Trans. Amer. Math. Soc. 6 (1905) 237-274. | JFM | MR

[17] Sakai T., Riemannian Geometry, Transl. Math. Monogr., vol. 149, American Mathematical Society, Providence, RI, 1996. | MR | Zbl

[18] Shiohama K., Tanaka M., Cut Loci and Distance Spheres on Alexandrov Surfaces, in: Actes De La Table Ronde De Géométrie Différentielle En L'honneur De Marcel Berger, Collection Soc. Math. France, vol. 1, Séminaires & Congrès, 1996, pp. 531-560. | MR | Zbl

[19] Shiohama K., Shioya T., Tanaka M., The Geometry of Total Curvature on Complete Open Surfaces, Cambridge Tracts in Mathematics, vol. 159, 2003. | MR | Zbl

[20] Sinclair R., Tanaka M., A Bound on the Number of Endpoints of the Cut Locus, LMS J. Comput. Math. 9 (2006) 21-39. | MR | Zbl

[21] Sinclair R., Tanaka M., The Cut Locus of a Two-Sphere of Revolution and Toponogov's Comparison Theorem, Tohoku Math. J. 59 (2) (2007) 379-399. | MR | Zbl

[22] Sugny D., Kontz C., Jauslin H., Time-Optimal Control of a Two-Level Dissipative Quantum System, Phys. Rev. A 76 (2007) 023419.

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