Free Access
Issue
ESAIM: COCV
Volume 20, Number 3, July-September 2014
Page(s) 864 - 893
DOI https://doi.org/10.1051/cocv/2013087
Published online 10 June 2014
  1. A.A. Agrachev, U. Boscain and M. Sigalotti, A Gauss–Bonnet-like Formula on Two-Dimensional Almost-Riemannian Manifolds. Discrete Contin. Dyn. Syst. A 20 (2008) 801-822. [CrossRef] [MathSciNet] [Google Scholar]
  2. V.I. Arnold, Mathematical Methods of Classical Mechanics, vol. 60. Translated from the Russian, edited by K. Vogtmann and A. Weinstein. 2nd edition. Grad. Texts Math. Springer-Verlag, New York (1989). [Google Scholar]
  3. L. Bates and F. Fassò, The conjugate locus for the Euler top. I. The axisymmetric case. Int. Math. Forum 2 (2007) 2109-2139. [MathSciNet] [Google Scholar]
  4. G.D. Birkhoff, Dynamical Systems, vol. IX. AMS Colloquium Publications (1927). [Google Scholar]
  5. A.V. Bolsinov and A.T. Fomenko, Integrable Hamiltonian Systems. Geometry, Topology, Classification. Translated from the Russian original 1999. Chapman & Hall/CRC, Boca Raton, FL (2004) 730. [Google Scholar]
  6. 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. Henri Poincaré Anal. Non Linéaire 26 (2009) 1081-1098. [CrossRef] [MathSciNet] [Google Scholar]
  7. 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]
  8. B. Bonnard, O. Cots, N. Shcherbakova and D. Sugny, The energy minimization problem for two-level dissipative quantum systems. J. Math. Phys. 51 (2010) 092705, 44. [CrossRef] [Google Scholar]
  9. U. Boscain, G. Charlot, J.-P. Gauthier, S. Guérin and H.-R. Jauslin, Optimal Control in laser-induced population transfer for two and three-level quantum systems. J. Math. Phys. 43 (2002) 2107-2132. [CrossRef] [MathSciNet] [Google Scholar]
  10. U. Boscain, T. Chambrion and G. Charlot, Nonisotropic 3-level Quantum Systems: Complete Solutions for Minimum Time and Minimum Energy. Discrete Contin. Dyn. Systems B 5 (2005) 957-990. [Google Scholar]
  11. U. Boscain and F. Rossi, Invariant Carnot-Caratheodory metrics on S3, SO(3), SL(2), and lens spaces. SIAM J. Control Optim. 47 (2008) 1851-1878. [CrossRef] [MathSciNet] [Google Scholar]
  12. J.-B. Caillau, O. Cots and J. Gergaud, Differential continuation for regular optimal control problems. Optim. Methods Softw. 27 (2011) 177–196. [Google Scholar]
  13. D. D’Alessandro, Introduction to quantum control and dynamics. Appl. Nonlinear Sci. Ser. Chapman & Hall/CRC (2008). [Google Scholar]
  14. H.T. Davis, Introduction to nonlinear differential and integral equations. Dover Publications Inc., New York (1962). [Google Scholar]
  15. P. Gurfil, A. Elipe, W. Tangren and M. Efroimsky, The Serret−Andoyer formalism in rigid-body dynamics I. Symmetries and perturbations. Regul. Chaotic Dyn. 12 (2007) 389-425. [CrossRef] [MathSciNet] [Google Scholar]
  16. J. Itoh and K. Kiyohara, The cut loci and the conjugate loci on ellipsoids. Manuscripta Math. 114 (2004) 247-264. [CrossRef] [MathSciNet] [Google Scholar]
  17. V. Jurdjevic, Geometric Control Theory, vol. 52. Camb. Stud. Adv. Math. Cambridge University Press, Cambridge (1997). [Google Scholar]
  18. N. Khaneja, R. Brockett and S.J. Glaser, Sub-Riemannian geometry and time optimal control of three spin systems: Quantum gates and coherence transfer. Phys. Rev. A 65 (2002) 032301. [CrossRef] [MathSciNet] [Google Scholar]
  19. M. Lara and S. Ferrer, Closed form Integration of the Hitzl-Breakwell problem in action-angle variables. IAA-AAS-DyCoSS1-01-02 (AAS 12-302), 27-39. [Google Scholar]
  20. D. Lawden, Elliptic Functions and Applications, vol. 80. Appl. Math. Sci. Springer-Verlag, New York (1989). [Google Scholar]
  21. M.H. Levitt, Spin dynamics, basis of Nuclear Magnetic Resonance, 2nd edition. John Wiley and sons (2007). [Google Scholar]
  22. H. Poincaré, Sur les lignes géodésiques des surfaces convexes. Trans. Amer. Math. Soc. 6 (1905) 237-274. [MathSciNet] [Google Scholar]
  23. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko, The mathematical theory of optimal processes. Interscience Publishers John Wiley & Sons, Inc., New York-London (1962). [Google Scholar]
  24. K. Shiohama, T. Shioya and M. Tanaka, The Geometry of Total Curvature on Complete Open Surfaces, vol. 159. Camb. Tracts Math. Cambridge University Press, Cambridge (2003). [Google Scholar]
  25. R. Sinclair and M. Tanaka, The cut locus of a two-sphere of revolution and Toponogov’s comparison theorem. Tohoku Math. J. 59 (2007) 379-399. [CrossRef] [MathSciNet] [Google Scholar]
  26. A.M. Vershik and V.Ya. Gershkovich, Nonholonomic Dynamical Systems, Geometry of Distributions and Variational Problems. in Dynamical Systems VII. In vol. 16 of Encyclopedia of Math. Sci. Springer Verlag (1991) 10-81. [Google Scholar]
  27. H. Yuan Geometry, optimal control and quantum computing, Ph.D. Thesis. Harvard (2006). [Google Scholar]
  28. H. Yuan, R. Zeier and N. Khaneja, Elliptic functions and efficient control of Ising spin chains with unequal coupling. Phys. Rev. A 77 (2008) 032340. [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.