Open Access
Volume 29, 2023
Article Number 60
Number of page(s) 34
Published online 31 July 2023
  1. V.I. Arnold and B.A. Khesin, Topological Methods in Hydrodynamics, Vol. 125 of Applied Mathematical Sciences. Springer-Verlag, New York (1998) 376. [Google Scholar]
  2. V.I. Arnold, Mathematical methods of classical mechanics. Translated from the Russian by K. Vogtmann and A. Weinstein. Graduate Texts in Mathematics, 2nd ed., Vol. 60. Springer-Verlag, New York (1989) 508. [Google Scholar]
  3. V.-I. Arnold, The theory of singularities and its applications, Lezioni Fermiane. Fermi Lectures, Accademia Nazionale dei Lincei, Rome, Scuola Normale Superiore, Pisa (1991) 73. [Google Scholar]
  4. C. Balsa, O. Cots, J. Gergaud and B. Wembe, Minimum energy control of passive tracers advection in point vortices flow, in: CONTROLO 2020. Lecture Notes in Electrical Engineering, Vol. 695, edited by J.A. Gonçalves, M. Braz-César and J.P. Coelho. Springer, Cham (2020). [Google Scholar]
  5. D. Bao, S.S. Chern and Z. Shen, An introduction to Riemann-Finsler geometry, in Vol. 200 of Graduate Texts in Mathematics. Springer-Verlag, New York (2000) 435. [Google Scholar]
  6. A.V. Bolsinov and A.T. Fomenko, Integrable Hamiltonian Systems, Geometry, Topology, Classification. Chapman and Hall/CRC, London (2004) 724. [Google Scholar]
  7. B. Bonnard and J.-B. Caillau, Geodesic flow of the averaged controlled Kepler equation. Forum Math. 21 (2009) 797–814. [CrossRef] [MathSciNet] [Google Scholar]
  8. B. Bonnard, J.-B. Caillau and G. Janin, Conjugate-cut loci and injectivity domains on two-spheres of revolution. ESAIM: COCV 19 (2013) 533–554. [CrossRef] [EDP Sciences] [Google Scholar]
  9. B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, Conjugate and cut loci of a two-sphere of revolution with application to optimal control. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 1081–1098. [CrossRef] [MathSciNet] [Google Scholar]
  10. B. Bonnard and M. Chyba, Singular trajectories and their role in control theory, In Vol. 40 of Mathematics & Applications. Springer-Verlag, Berlin (2003) 357. [Google Scholar]
  11. B. Bonnard, O. Cots and N. Shcherbakova, Riemannian metrics on 2D-manifolds related to the Euler–Poinsot rigid body motion. ESAIM: COCV 20 (2014) 864–893. [CrossRef] [EDP Sciences] [Google Scholar]
  12. B. Bonnard, O. Cots, J. Gergaud and B. Wembe, Abnormal geodesics in 2D-zermelo navigation problems in the case of revolution and the fan shape of the small time balls. Syst. Control Lett. 161 (2022) 105140. [CrossRef] [Google Scholar]
  13. B. Bonnard, O. Cots and B. Wembe, A zermelo navigation problem with a vortex singularity. ESAIM Control Optim. Calc. Var. 27 (2021) 37. [Google Scholar]
  14. B. Bonnard and I. Kupka, Théorie des singularités de l’application entrée/sortie et optimalité des trajectoires singulières dans le problème du temps minimal. Forum Math. 5 (1993) 111–159. [CrossRef] [MathSciNet] [Google Scholar]
  15. B. Bonnard, J. Rouot and B. Wembe, Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies. Math. Control Related Fields (2022) [Google Scholar]
  16. A.E. Bryson and Y.C. Ho, Applied optimal control. Hemisphere Publishing, New York (1975) 481. [Google Scholar]
  17. J.-B. Caillau, O. Cots and J. Gergaud, Differential continuation for regular optimal control problems. Optim. Methods Softw. 27 (2011) 177–196. [Google Scholar]
  18. C. Carathéodory, Calculus of Variations and Partial Differential Equations of the First Order, Part 1, Part 2. Holden-Day, San Francisco, California, 1965–1967; Reprint: 2nd AMS printing, AMS Chelsea Publishing, Providence, RI, USA (2001) 412. [Google Scholar]
  19. M.P. Do Carmo, Riemannian geometry, In Birkhäuser, Mathematics: Theory & Applications, 2nd edn. (1988) 300. [Google Scholar]
  20. G. Godbillon, Feuilletages, études géométriques, in Progr. Math. 98. Birkhäuser, Boston (1991) 475. [Google Scholar]
  21. W.B. Gordon, A minimizing property of Keplerian orbits. AMS 99 (1977) 962–971. [Google Scholar]
  22. V. Grines, E. Gurevich, O. Pochinka and D. Malyshev, On topological classification of Morse-Smale diffeomorphisms on the sphere Sn, (n > 3). Nonlinearity 33 (2020) 7088–7113. [CrossRef] [MathSciNet] [Google Scholar]
  23. R. Hama, J. Kasemsuwan and S. V. Sabau, The cut locus of a Randers rotational 2-sphere of revolution, Publ. Math. Debrecen 93 (2018) 387–412. [CrossRef] [MathSciNet] [Google Scholar]
  24. J. Itoh and K. Kiyohara, The cut loci and the conjugate loci on ellipsoids. Manuscripta Math. 114 (2004) 247–264. [CrossRef] [MathSciNet] [Google Scholar]
  25. I. Kupka, Abnormal extremals. Preprint (1992). [Google Scholar]
  26. R.K. Meyer and G.R. Hall, Introduction to Hamiltonian dynamical systems and the N-body problem. Appl. Math. Sci. 90 (1992) 292. [Google Scholar]
  27. H. Poincaré, Sur les lignes géodésiques des surfaces convexes. (French) [On the geodesic lines of convex surfaces]. Trans. Amer. Math. Soc. 6 (1905) 237–274. [MathSciNet] [Google Scholar]
  28. L.S. Pontryagin, V.G. Boltyanskiĭ, R.V. Gamkrelidze and E.F. Mishchenko, The Mathematical Theory of Optimal Processes. Translated from the Russian by K.N. Trirogoff, edited by L.W. Neustadt. Interscience Publishers John Wiley & Sons, Inc., New York-London (1962) 360. [Google Scholar]
  29. C.L. Siegel and J.K. Moser, Lectures on celestial mechanics. Translation by Charles I. Kalme. Die Grundlehren der mathematischen Wissenschaften, Band 187. Springer-Verlag, New York-Heidelberg (1971) 290. [Google Scholar]
  30. H.J. Sussmann, The structure of time-optimal trajectories for single-input systems in the plane: the C nonsingular case. SIAM J. Control Optim. 25 (1987) 433–465. [CrossRef] [MathSciNet] [Google Scholar]
  31. H.J. Sussmann, Regular synthesis for time-optimal control of single-input real analytic systems in the plane. SIAM J. Control Optim. 25 (1987) 1145–1162. [CrossRef] [MathSciNet] [Google Scholar]
  32. R.J. Walker, Algebraic Curves. Springer-Verlag, New York (1978) 201. [Google Scholar]
  33. B. Wembe, Méthodes Géométriques et Numériques en Contrôle Optimal et Problèmes de Zermelo sur les Surfaces de Révolution – Applications, PhD thesis, Université Toulouse Paul Sabatier, Toulouse (2021). [Google Scholar]
  34. E. Zermelo, Über das Navigations problem bei ruhender oder veränderlicher wind-verteilung. Z. Angew. Math. Mech. 11 (1931) 114–124. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.