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Preface
A geometric fractional monodromy theorem
1. | Department of Mathematics, University of Groningen, PO Box 407, 9700 AK, Groningen, Netherlands |
2. | Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom |
References:
[1] |
Y. Colin de Verdière and San Vũ Ngoc, Singular Bohr-Sommerfeld rules for 2D integrable systems,, Ann. Sci. Éc. Norm. Sup., 36 (2003), 1.
|
[2] |
R. H. Cushman and J. J. Duistermaat, Non-Hamiltonian monodromy,, J. Diff. Eqs., 172 (2001), 42.
doi: 10.1006/jdeq.2000.3852. |
[3] |
R. H. Cushman, H. Dullin, H. Hanßmann and S. Schmidt, The 1:±2 resonance,, Regular and Chaotic Dynamics, 12 (2007), 642.
doi: 10.1134/S156035470706007X. |
[4] |
R. H. Cushman and San Vũ Ngoc, Sign of the monodromy for Liouville integrable systems,, Annales Henri Poincaré, 3 (2002), 883.
doi: 10.1007/s00023-002-8640-7. |
[5] |
R. Devaney, "An Introduction to Chaotic Dynamical Systems,'', Benjamin-Cummings, (1986).
|
[6] |
J. J. Duistermaat, On global action-angle coordinates,, Comm. Pure Appl. Math., 33 (1980), 687.
doi: 10.1002/cpa.3160330602. |
[7] |
K. Efstathiou, R. H. Cushman and D. A. Sadovskií, Fractional monodromy in the 1:-2 resonance,, Advances in Mathematics, 209 (2007), 241.
doi: 10.1016/j.aim.2006.05.006. |
[8] |
A. Giacobbe, Fractional monodromy: Parallel transport of homology cycles,, Diff. Geom. and Appl., 26 (2008), 140.
doi: 10.1016/j.difgeo.2007.11.011. |
[9] |
O. V. Lukina, "Geometry of Torus Bundles in Integrable Hamiltonian Systems,'', Ph.D thesis, (2008). Google Scholar |
[10] |
O. V. Lukina, F. Takens and H. W. Broer, Global properties of integrable Hamiltonian systems,, Regular and Chaotic Dynamics, 13 (2008), 602.
doi: 10.1134/S1560354708060105. |
[11] |
N. N. Nekhoroshev, Action-angle variables and their generalizations,, Trans. Moscow Math. Soc., 26 (1972), 180.
|
[12] |
N. N. Nekhoroshev, Fractional monodromy in the case of arbitrary resonances,, Sbornik: Mathematics, 198 (2007), 383.
doi: 10.1070/SM2007v198n03ABEH003841. |
[13] |
N. N. Nekhoroshev, Fuzzy fractional monodromy and the section-hyperboloid,, Milan J. Math., 76 (2008), 1.
doi: 10.1007/s00032-008-0085-0. |
[14] |
N. N. Nekhoroshev, D. A. Sadovskií and B. I. Zhilinskií, Fractional monodromy of resonant classical and quantum oscillators,, Comptes Rendus Acad. Sci. Paris, 335 (2002), 985.
|
[15] |
N. N. Nekhoroshev, D. A. Sadovskií and B. I. Zhilinskií, Fractional Hamiltonian monodromy,, Annales Henri Poincaré, 7 (2006), 1099.
doi: 10.1007/s00023-006-0278-4. |
[16] |
D. Sugny, P. Mardešić, M. Pelletier, A. Jebrane and H. R. Jauslin, Fractional Hamiltonian monodromy from a Gauss-Manin monodromy,, J. Math. Phys., 49 (2008), 042701.
doi: 10.1063/1.2863614. |
[17] |
San Vũ Ngoc, Quantum monodromy in integrable systems,, Communications in Mathematical Physics, 203 (1999), 465.
doi: 10.1007/s002200050621. |
[18] |
N. T. Zung, A note on focus-focus singularities,, Diff. Geom. and Appl., 7 (1997), 123.
doi: 10.1016/S0926-2245(96)00042-3. |
[19] |
Nguyen Tien Zung, Symplectic topology of integrable Hamiltonian systems, I: Arnold-Liouville with singularities,, Comp. Math., 101 (1996), 179.
|
show all references
References:
[1] |
Y. Colin de Verdière and San Vũ Ngoc, Singular Bohr-Sommerfeld rules for 2D integrable systems,, Ann. Sci. Éc. Norm. Sup., 36 (2003), 1.
|
[2] |
R. H. Cushman and J. J. Duistermaat, Non-Hamiltonian monodromy,, J. Diff. Eqs., 172 (2001), 42.
doi: 10.1006/jdeq.2000.3852. |
[3] |
R. H. Cushman, H. Dullin, H. Hanßmann and S. Schmidt, The 1:±2 resonance,, Regular and Chaotic Dynamics, 12 (2007), 642.
doi: 10.1134/S156035470706007X. |
[4] |
R. H. Cushman and San Vũ Ngoc, Sign of the monodromy for Liouville integrable systems,, Annales Henri Poincaré, 3 (2002), 883.
doi: 10.1007/s00023-002-8640-7. |
[5] |
R. Devaney, "An Introduction to Chaotic Dynamical Systems,'', Benjamin-Cummings, (1986).
|
[6] |
J. J. Duistermaat, On global action-angle coordinates,, Comm. Pure Appl. Math., 33 (1980), 687.
doi: 10.1002/cpa.3160330602. |
[7] |
K. Efstathiou, R. H. Cushman and D. A. Sadovskií, Fractional monodromy in the 1:-2 resonance,, Advances in Mathematics, 209 (2007), 241.
doi: 10.1016/j.aim.2006.05.006. |
[8] |
A. Giacobbe, Fractional monodromy: Parallel transport of homology cycles,, Diff. Geom. and Appl., 26 (2008), 140.
doi: 10.1016/j.difgeo.2007.11.011. |
[9] |
O. V. Lukina, "Geometry of Torus Bundles in Integrable Hamiltonian Systems,'', Ph.D thesis, (2008). Google Scholar |
[10] |
O. V. Lukina, F. Takens and H. W. Broer, Global properties of integrable Hamiltonian systems,, Regular and Chaotic Dynamics, 13 (2008), 602.
doi: 10.1134/S1560354708060105. |
[11] |
N. N. Nekhoroshev, Action-angle variables and their generalizations,, Trans. Moscow Math. Soc., 26 (1972), 180.
|
[12] |
N. N. Nekhoroshev, Fractional monodromy in the case of arbitrary resonances,, Sbornik: Mathematics, 198 (2007), 383.
doi: 10.1070/SM2007v198n03ABEH003841. |
[13] |
N. N. Nekhoroshev, Fuzzy fractional monodromy and the section-hyperboloid,, Milan J. Math., 76 (2008), 1.
doi: 10.1007/s00032-008-0085-0. |
[14] |
N. N. Nekhoroshev, D. A. Sadovskií and B. I. Zhilinskií, Fractional monodromy of resonant classical and quantum oscillators,, Comptes Rendus Acad. Sci. Paris, 335 (2002), 985.
|
[15] |
N. N. Nekhoroshev, D. A. Sadovskií and B. I. Zhilinskií, Fractional Hamiltonian monodromy,, Annales Henri Poincaré, 7 (2006), 1099.
doi: 10.1007/s00023-006-0278-4. |
[16] |
D. Sugny, P. Mardešić, M. Pelletier, A. Jebrane and H. R. Jauslin, Fractional Hamiltonian monodromy from a Gauss-Manin monodromy,, J. Math. Phys., 49 (2008), 042701.
doi: 10.1063/1.2863614. |
[17] |
San Vũ Ngoc, Quantum monodromy in integrable systems,, Communications in Mathematical Physics, 203 (1999), 465.
doi: 10.1007/s002200050621. |
[18] |
N. T. Zung, A note on focus-focus singularities,, Diff. Geom. and Appl., 7 (1997), 123.
doi: 10.1016/S0926-2245(96)00042-3. |
[19] |
Nguyen Tien Zung, Symplectic topology of integrable Hamiltonian systems, I: Arnold-Liouville with singularities,, Comp. Math., 101 (1996), 179.
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