Open Access
Volume 27, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Article Number S10
Number of page(s) 37
Published online 01 March 2021
  1. A.A. Agrachev and Y.L. Sachkov, Control theory from the geometric viewpoint. Vol. 87 of Encyclopaedia of Mathematical Sciences. Springer-Verlag, Berlin (2004). [Google Scholar]
  2. V.I. Arnold and B.A. Khesin, Topological Methods in Hydrodynamics. Vol. 125 of Applied Mathematical Sciences. Springer-Verlag, New York (1998). [Google Scholar]
  3. D. Bao, S.-S. Chern and Z. Shen, An Introduction to Riemann–Finsler Geometry. Vol. 200 of Graduate Texts in Mathematics. Springer-Verlag, New York (2000). [Google Scholar]
  4. D. Bao, C. Robles and Z. Shen, Zermelo navigation on Riemannian manifolds. J. Differ. Geom. 66 (2004) 377–435. [Google Scholar]
  5. V.G. Boltyanskii, Sufficient conditions for optimality and the justification of the dynamic programming method. SIAM J. Control Optim. 4 (1966) 326–361. [Google Scholar]
  6. A.V. Bolsinov, and A.T. Fomenko, Integrable Hamiltonian Systems Geometry, Topology, Classification Chapman and Hall/CRC, London (2004). [Google Scholar]
  7. 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. [Google Scholar]
  8. B. Bonnard and M. Chyba, Singular Trajectories and their Role in Control Theory. Vol. 40 of Mathematics & Applications. Springer-Verlag, Berlin (2003). [Google Scholar]
  9. B. Bonnard and D. Sugny, Optimal Control with Applications in Space and Quantum Dynamics. Vol. 5 of Applied Mathematics. AIMS (2012). [Google Scholar]
  10. B. Bonnard, L. Faubourg and E. Trélat, Mécanique céleste et contrôle des véhicules spatiaux. Vol. 51 of Mathématiques & Applications. Springer-Verlag, Berlin (2006). [Google Scholar]
  11. B. Bonnard, J.-B. Caillau and E. Trélat, Second order optimality conditions in the smooth case and applications in optimal control. ESAIM: COCV 13 (2007) 207–236. [CrossRef] [EDP Sciences] [Google Scholar]
  12. A.E. Bryson and Y.-C. Ho, Applied Optimal Control. Hemisphere Publishing, New York (1975). [Google Scholar]
  13. J.-B. Caillau, O. Cots and J. Gergaud, Differential continuation for regular optimal control problems. Optim. Methods Softw. 27 (2011) 177–196. [Google Scholar]
  14. R.C. Calleja, E.J. Doedel and C. García-Azpeitia, Choreographies in the n-vortex problem. Regul. Chaot. Dyn. 23 (2018) 595–612. [Google Scholar]
  15. 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). [Google Scholar]
  16. L. Cesari, Optimization-theory and Applications: Problems with Ordinary Differential Equations. Vol. 17 of Applications of Mathematics. Springer-Verlag, New York (1983). [Google Scholar]
  17. A. Chenciner, J. Gerver, R. Montgomery and C. Simó, Simple Choreographic Motions of N Bodies: A Preliminary Study, edited by P. Newton, P. Holmes, A. Weinstein. Geometry, Mechanics, and Dynamics. Springer New York, NY (2002) 287–308. [Google Scholar]
  18. O. Cots, Contrôle optimal géométrique: méthodes homotopiques et applications. Ph.D. thesis, Université de Bourgogne, Dijon (2012). [Google Scholar]
  19. M.P. Do Carmo, Riemannian Geometry. Mathematics: Theory & applications, 2nd ed. Birkhäuser (1988). [Google Scholar]
  20. G. Godbillon, Feuilletages, études géométriques. Vol. 98 of Progr. Math. Birkhäuser, Boston (1991). [Google Scholar]
  21. V.V. Goryunov and V.M. Zakalyukin, Lagrangian and Legendrian singularities, in Real and Complex Singularities. Trends in Mathematics, edited by J.P. Brasselet and M.A.S. Ruas. Birkhäuser, Basel (2006).. [Google Scholar]
  22. 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. [Google Scholar]
  23. G. Hector, Les feuilletages de Reeb, L’Ouvert. Num. 76 spécial Georges Reeb. IREM de Strasbourg, Strasbourg (1994) 93–111. [Google Scholar]
  24. H.V. Helmholtz, On integrals of hydrodynamics equations, corresponding to vortex motions. Russ. J. Nonlin. Dyn. 2 (2006) 473–507. [Google Scholar]
  25. J. Itoh and K. Kiyohara, The cut loci and the conjugate loci on ellipsoids. Manuscripta Math. 114 (2004) 247–264. [Google Scholar]
  26. V. Jurdjevic, Geometric Control Theory. Vol. 52 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (1997). [Google Scholar]
  27. G.R. Kirchhoff, Vorlesungen uber mathematische Physik. Mechanik, Leipzig, Teubner (1876). [Google Scholar]
  28. A.J. Krener, The high order maximal principle and its application to singular extremals. SIAM J. Control Optim. 15 (1977) 256–293. [Google Scholar]
  29. K. Meyer, G. Hall and D.C. Offin, Introduction to Hamiltonian Dynamical Systems and the N-Body Problem. Vol. 90 of Applied Mathematical Sciences. Springer-Verlag, New York (2009). [Google Scholar]
  30. P.K. Newton, The N-Vortex Problem – Analytical Techniques. Vol. 145 of Applied Mathematical Sciences. Springer-Verlag, New York (2001) 420. [Google Scholar]
  31. H. Poincaré, Œuvres. Gauthier-Villars (1952). [Google Scholar]
  32. 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).. [Google Scholar]
  33. B. Protas, Vortex Dynamics Models in Flow Control Problems. Nonlinearity 21 (2008) R203. IOP Science (2008).. [Google Scholar]
  34. P.G. Saffman, Vortex Dynamics. Cambridge University Press (1992). [Google Scholar]
  35. U. Serres, Géométrie et classification par feedback des systèmes de contrôle non linéaires de basse dimension. Ph.D. thesis, Université de Bourgogne, Dijon (2006) 51–62. [Google Scholar]
  36. D. Vainchtein and I. Mezi, Optimal control of a co-rotating vortex pair: averaging and impulsive control. Physica D 192 (2004) 63–82. [Google Scholar]
  37. E. Zermelo, Über das Navigations problem bei ruhender oder veränderlicher wind-verteilung. Z. Angew. Math. Mech. 11 (1931) 114–124. [Google Scholar]

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