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Original Articles

Quantum monodromy and its generalizations and molecular manifestations

&
Pages 2595-2615 | Received 19 Jan 2006, Accepted 20 Feb 2006, Published online: 28 Nov 2010

References

  • Duistermaat, JJ , 1980. Comm. Pure Appl. Math. 33 (1980), p. 687.
  • Nekhoroshev, NN , 1972. Trans. Moscow Math. Soc. 26 (1972), p. 180.
  • Cushman, RH , and Duistermaat, JJ , 1988. Bull. Am. Math. Soc. 19 (1988), p. 475.
  • Cushman, RH , 1983. Centr. Wiskd. Informat. Newslett. 1 (1983), p. 4.
  • Bates, LM , and Cushman, RH , 1997. Global Aspects of Classical Integrable Systems . Basel: Birkhäuser; 1997.
  • Cushman, RH , and Sadovskií, DA , 1999. Europhys. Lett. 47 (1999), p. 1.
  • Cushman, RH , and Sadovskií, DA , 2000. Physica D 142 (2000), p. 166.
  • Efstathiou, K , Cushman, RH , and Sadovskií, DA , 2004. Physica D 194 (2004), p. 250.
  • Sadovskií, DA , and Zhilinskií, BI , 1999. Phys. Lett. A 256 (1999), p. 235.
  • Grondin, L , Sadovskií, DA , and Zhilinskií, BI , 2002. Phys. Rev. A 142 (2002), p. 012105.
  • Child, MS , Weston, T , and Tennyson, J , 1999. Molec. Phys. 96 (1999), p. 371.
  • Zobov, NF , Shirin, SV , Polyansky, OL , Tennyson, J , Coheur, P-F , Bernath, PF , Carleer, M , and Colin, R , 2005. Chem. Phys. Lett. 414 (2005), p. 193.
  • Waalkens, H , Junge, A , and Dullin, HR , 2003. J. Phys. A Math. Gen. 36 (2003), p. L307.
  • Waalkens, H , Dullin, HR , and Richter, PH , 2004. Physica D 196 (2004), p. 265.
  • Joyeux, M , Sadovskií, DA , and Tennyson, J , 2003. Chem. Phys. Lett. 382 (2003), p. 439.
  • Efstathiou, K , Joyeux, M , and Sadovskií, DA , 2004. Phys. Rev. A 69 (2004), p. 032504.
  • Cushman, RH , Dullin, HR , Giacobbe, A , Holm, DD , Joyeux, M , Lynch, P , Sadovskií, DA , and Zhilinskií, BI , 2004. Phys. Rev. Lett. 93 (2004), p. 024302.
  • Giacobbe, A , Cushman, RH , Sadovskií, DA , and Zhilinskií, BI , 2004. J. Math. Phys. 45 (2004), p. 5076.
  • Cooper, CD , and Child, MS , 2005. Phys. Chem. Chem. Phys. 7 (2005), p. 2731, note that figures 7 and 8 of this paper are corrected in 27.
  • Kozin, IN , and Roberts, RM , 2003. J. Chem. Phys. 118 (2003), p. 10523.
  • Arango, CA , Kennerly, WW , and Ezra, GS , 2004. Chem. Phys. Lett. 392 (2004), p. 486, J. Chem. Phys. 122 184303 (2005).
  • Efstathiou, K , 2004. Metamorphoses of Hamiltonian Systems with Symmetry, Lecture Notes in Mathematics . Vol. Vol. 1864. Heidelberg: Springer-Verlag; 2004.
  • Vũ, S , 1999. Ngc, Comm. Math. Phys. 203 (1999), p. 465.
  • Nekhoroshev, NN , Sadovskií, DA , and Zhilinskií, BI , 2006. Ann. Henri Poincaré (2006), accepted for publication.
  • Zhilinskií, BI , 2005. Acta Appl. Math. 87 (2005), p. 281.
  • Zhilinskii, BI , 2006. Monastyrsky, M , ed. Topology in Condensed Matter, Springer Series in Solid State Sciences . Vol. Vol. 150. Berlin: Springer; 2006. p. 165.
  • Child, M , Adv. Chem. Phys., (in press).
  • Audin, M , 1991. Topology of Torus Actions on Symplectic Manifolds . Boston: Birkhäuser; 1991.
  • Guillemin, V , 1994. Moment Maps and Combinatorial Invariants of Hamiltonian Tn-spaces . Boston: Birkhäuser; 1994.
  • Souriau, J-M , 1970. "Structure of Dynamical Systems: A Symplectic View of Physics". In: Cushman, RH , and Tuynman, GM , eds. Structure des Systèmes Dynamiques . Paris: Dunod; 1970, translated by C. H. Cushman-de Vries (Birkhäuser, Boston, 1997) [Original French edition:].
  • Arnol'd, VlI , 1989. "Mathematical Methods of Classical Mechanics". In: Graduated Texts in Mathematics, . Vol. Vol. 60. New York: Springer-Verlag; 1989, in the series, translated by K. Vogtmann and A. Weinstein.
  • Broer, H , Cushman, RH , Fassò, F , and Takens, F , 2002. (2002), preprint arXiv:math.DS/0210043.
  • Rink, B , 2004. Nonlinearity 17 (2004), p. 347.
  • Gutzwiller, MC , 1990. Chaos in Classical and Quantum Mechanics, Series in Interdisciplinary Applied Mathematics . Vol. Vol. 1. New York: Springer; 1990, Chapt. 14.
  • Matveev, VS , 1996. Sb. Math. 187 (1996), p. 495.
  • Lerman, LM , and Umanskií, Ya L , 1998. "Four Dimensional Integrable Hamiltonian Systems with Simple Singular Points". In: Translations of Mathematical Monographs . Vol. Vol. 176. Providence, RI: American Mathematics Society; 1998, in the series.
  • Cushman, RH , and Duistermaat, JJ , 2001. J. Diff. Eq. 172 (2001), p. 42.
  • Zung, NT , 1997. Diff. Geom. Appl. 7 (1997), p. 123, Lett. Math. Phys.60 87 (2002).
  • Bolsinov, AV , and Fomenko, AT , 2004. Integrable Hamiltonian Systems. Geometry, Topology, Classification . London: Chapman & Hall/CRC; 2004.
  • Nekhoroshev, NN , Sadovskií, DA , and Zhilinskií, BI , 2002. CR Acad. Sci. Paris Ser. I 335 (2002), p. 985.
  • Efstathiou, K , Cushman, RH , and Sadovskií, DA , 2006. Adv. Math. (2006), accepted for publication.
  • Colin de Verdier, Y , and Vũ Ngoc, S , 2003. Ann. Ec. Norm. Sup. 36 (2003), p. 1.
  • Fulton, N , Tennyson, J , Sadovskií, DA , and Zhilinskií, BI , 1993. J. Chem. Phys. 99 (1993), p. 906.
  • Kozin, IN , Sadovskií, DA , and Zhilinskií, BI , 2005. Spectrochim. Acta A 61 (2005), p. 2867.
  • Efstathiou, K , and Sadovskií, DA , 2004. Nonlinearity 17 (2004), p. 415.
  • Efstathiou, K , Cushman, RH , and Sadovskií, DA , 2003. Proc. R. Soc. Ser. A 459 (2003), p. 2997.
  • Efstathiou, K , Sadovskií, DA , and Zhilinskií, BI , 2004. SIADS (SIAM J. Appl. Dyn. Syst.) 3 (2004), p. 261.
  • Bates, LM , 1988. Proc. R. Soc. Edinburgh A 110 (1988), p. 27.
  • Gross, M , 1998. Saito, M-H , Shimuzu, Y , and Ueno, K , eds. Integrable Systems and Algebraic Geometry . Singapore: World Scientific; 1998. pp. 156–193.
  • Gross, M , 1999. Surveys in Differential Geometry . Somerville, MA: International Press; 1999. pp. 341–403.
  • Gross, M , 2001. Invent. Math. 144 (2001), p. 75.
  • Bates, LR , 1991. J. Appl. Math. Phys. (ZAMP) 42 (1991), p. 837.
  • Child, M , 1998. J. Phys. A: Math. Gen. 31 (1998), p. 657.
  • Dixon, RN , 1964. Trans. Faraday Soc. 60 (1964), p. 1363.
  • Holm, DD , and Lynch, P , 2002. SIAM J. Appl. Dyn. Syst. 1 (2002), p. 44.
  • Lynch, P , 2002. Int. J. Nonlin. Mech. 37 (2002), p. 345.
  • Dullin, H , Giacobbe, A , and Cushman, RH , 2004. Physica D 190 (2004), p. 15.
  • Xiao, L , and Kellman, ME , 1990. J. Chem. Phys. 93 (1990), p. 5805.
  • Zhou, C , Xie, D , Chen, R , Yan, G , Guo, H , Tyng, V , and Kellman, M , 2002. Spectrochim. Acta A 58 (2002), p. 727.
  • Joyeux, M , Farantos, SC , and Schinke, R , 2002. J. Phys. Chem. A 106 (2002), p. 5407.
  • Efstathiou, K , and Sadovskií, DA , 2005. "Geometric Mechanics and Symmetry". In: Montaldi, J , and Ratiu, T , eds. The Peyresq Lectures, London Mathematical Society . Lecture Note Series No. 306. Cambridge, UK: Cambridge University Press; 2005.
  • van der Meer, JC , 1985. "The Hamiltonian Hopf Bifurcation". In: Lecture Notes in Mathematics . Vol. Vol. 1160. New York: Springer; 1985, in the series.
  • Sugny, D , Joyeux, M , and Jauslin, HR , , private communication.
  • Giacobbe, A , , private communication.

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