A partial list of papers/books that cite my work

Last  updated: 23/Dec/2002

Nguyen Tien Zung

Preprints
  1. Bordemann, M.; Makhlouf, A.; Petit, T. Deformation par quantification et rigidite des algebres enveloppantes,  preprint math.RA/0211416.
  2. Colin de Verdière, Yves. Singular Lagrangian manifolds and semi-classical analysis, preprint 2001, to appear in Duke Math. J.
  3. Colin de Verdière, Y.; Vu Ngoc San, Singular Bohr-Sommerfeld rules for 2D integrable systems, preprint math.AP/0005264 (2000), to appear in Annales ENS.
  4. Curras-Bosch, C.; Miranda, E. Symplectic linearization of singular Lagrangian foliations in M4, preprint (2001), to appear in Diff. Geom. Appl.
  5. Dufour, J.-P.; Zhitomirskii, M. Nambu structures and integrable 1-forms, preprint math.DG/0002167 (2000), to appear in Let. Math. Phys.
  6. Ghrist, R.; Komendarczyk, R. Toplological features of inviscid flows, preprint (2001).
  7. Martinez Torres, David. Global classification of generic multi-vector fields of top degree, preprint math.DG/0209374 (2002).
  8. Rink, Bob. A cantor set of tori with monodromy near a focus-focus singularity, preprint Utrecht  (2001).
  9. Symington, Margaret. Four dimensions from two in symplectic topology, preprint math.SG/0210033 (2002).
  10. Vivolo, Olivier.  The mondromy of the Lagrange Top and the Picard-Lefschetz formula (2001), to appear in J. Geom. Phys.
  11. Wade, Aissa.  Vinogradov Bracket and Nambu-Dirac Structures on Lie Algebroids, preprint math.SG/0204310.
2002
  1. Audin, Michèle. Hamiltonian monodromy via Picard-Lefschetz theory,  Comm. Math. Phys. 229 (2002), no. 3, 459--489.
  2. Ferrer, Sebastián; Hanßmann, Heinz ; Palacián, Jesús; Yanguas, Patricia . On perturbed oscillators in 1-1-1 resonance: the case of axially symmetric cubic potentials. J. Geom. Phys. 40 (2002), no. 3-4, 320--369.
  3. Jovanovic, B. On the integrability of geodesic flows of submersion metrics,  Lett. Math. Phys. 61 (2002), no. 1, 29--39.
  4. Rink, Bob. Direction reversing travelling waves in the Fermi-Pasta-Ulam chain. nlin.SI/0110015, J. Nonlinear Science 22 (2002) 479-504.
  5. Vinogradov, A. M.; Vinogradov, M. M. Graded multiple analogs of Lie algebras. Symmetries of differential equations and related topics. Acta Appl. Math. 72 (2002), no. 1-2, 183--197.
  6. Vu Ngoc, San. On semi-global invariants for focus-focus singularities,  Topology, vol 42, number 2, pp. 365--380, 2002 ).
  7. Waalkens, Holger; Dullin, Holger R. Quantum monodromy in prolate ellipsoidal billiards. Ann. Physics 295 (2002), no. 1, 81--112.

2001
  1. Cushman, R.; Duistermaat, J. J. Non-Hamiltonian monodromy. J. Differential Equations 172 (2001), no. 1, 42--58.
  2. Meinrenken, E. Symplectic geometry. Lecture Notes, University of Toronto (2001).
  3. Smith, Ivan. Torus fibrations on symplectic four-manifolds. Turkish J. Math. 25 (2001), no. 1, 69--95.
  4. Symington, Margaret. Generalized rational symplectic blowdown, Algebr. Geom. Topol. 1 (2001) 503-518.
  5. Zhilinskii, B.I.Qualitative features of quantum finie particle systems, Proceedings of Andronov memorial conference, Frontiers of Nonlinear Science, Nozhnii Novgorod (2001).

2000
  1. Bolsinov, A. V.; Richter, P. H.; Fomenko, A. T. The method of loop molecules and the topology of the Kovalevskaya top. Sb. Mat. 191 (2000), no. 2, 3--42, 151-188.
  2. Campos, B.; Martínez Alfaro, J. ; Vindel, P. Bifurcations of links of periodic orbits in non-singular Morse-Smale systems with a rotational symmetry on $S\sp 3$. Topology Appl. 102 (2000), no. 3, 279--295.
  3. Cushman, R. H.; Sadovskií, D. A. Monodromy in the hydrogen atom in crossed fields. Phys. D 142 (2000), no. 1-2, 166--196.
  4. Dufour, Jean-Paul. Singularities of Poisson and Nambu structures. Poisson geometry (Warsaw, 1998), 61--68, Banach Center Publ., 51, Polish Acad. Sci., Warsaw, 2000.
  5. Etnyre, John; Ghrist, Robert. Contact topology and hydrodynamics. I. Beltrami fields and the Seifert conjecture. Nonlinearity 13 (2000), no. 2, 441--458.
  6. Grabowski, J.; Marmo, G. On Filippov algebroids and multiplicative Nambu-Poisson structures. Differential Geom. Appl. 12 (2000), no. 1, 35--50.
  7. Lerman, L. M. Isoenergetical structure of integrable Hamiltonian systems in an extended neighborhood of a simple singular point: three degrees of freedom. Methods of qualitative theory of differential equations and related topics, Supplement, 219--242 , Amer. Math. Soc. Transl. Ser. 2, 200, Amer. Math. Soc., Providence, RI, 2000. [Comment: Unfortunately, the author misinterpreted my decomposition theorem, and rediscovered some special cases of it].
  8. Ouazzani-T. H, A.; Dekkaki, S.; Kharbach, J.; Ouazzani-Jamil, M. Bifurcation sets of the motion of a heavy rigid body around a fixed point in Goryatchev-Tchaplygin case. Nuovo Cimento Soc. Ital. Fis. B (12) 115 (2000), no. 10, 1175--1193.
  9. Vaisman, Izu. Nambu-Lie groups. J. Lie Theory 10 (2000), no. 1, 181--194.
  10. Vu Ngoc, San. Bohr-Sommerfeld conditions for integrable systems with critical manifolds of focus-focus type. Comm. Pure Appl. Math.53 (2000), no. 2, 143--217.
  11. Wade, Aïssa. Conformal Dirac structures. Lett. Math. Phys. 53 (2000), no. 4, 331--348.

1999
  1. Bates, Larry; Cushman, Richard. What is a completely integrable nonholonomic dynamical system? Proceedings of the XXX Symposium on Mathematical Physics (Torun, 1998). Rep. Math. Phys. 44 (1999), no. 1-2, 29--35.
  2. Bolsinov, A. V.; Fomenko, A. T. Integrable Hamiltonian systems. Geometry, topology, classification. Vol. I,II (Russian). Izhevsk,1999. 1: 444 pp.; 2: 447 pp. ISBN: 5-7029-0352-8.
  3. Etnyre, John B.; Ghrist, Robert W. Stratified integrals and unknots in inviscid flows. Geometry and topology in dynamics (Winston-Salem, NC, 1998/San Antonio, TX, 1999), 99--111, Contemp. Math., 246, Amer. Math. Soc., Providence, RI, 1999.
  4. Grabowski, J.; Marmo, G. Remarks on Nambu-Poisson and Nambu-Jacobi brackets. J. Phys. A 32 (1999), no. 23, 4239--4247.
  5. Kudryavtseva, E. A. Realization of smooth functions on surfaces as height functions. Sb. Math. 190 (1999), no. 3-4, 349--405.
  6. Médan, Christine. Degenerate invariant manifolds of some completely integrable systems. Math. Z. 232 (1999), no. 4, 665--689.
  7. Nakanishi, N. A survey of Nambu-Poisson geometry. Towards 100 years after Sophus Lie (Kazan, 1998). Lobachevskii J. Math. 4 (1999), 5--11 (electronic).
  8. Vaisman, Izu. A survey on Nambu-Poisson brackets. Acta Math. Univ. Comenian. (N.S.) 68 (1999), no. 2, 213--241.
  9. Vu Ngoc, San. Quantum monodromy in integrable systems. Comm. Math. Phys. 203 (1999), no. 2, 465--479.

1998
  1. Bolsinov, A. V.; Matveev, V. S.; Fomenko, A. T. Two-dimensional Riemannian metrics with an integrable geodesic flow. Local and global geometries. Sb. Math. 189 (1998), no. 9-10, 1441--1466.
  2. Brailov, Yu. A. Algebraic aspects of classification of singularities in Hamiltonian systems. Regul. Chaotic Dyn. 4 (1999), no. 3, 30--34.
  3. Ghrist, Robert W. Chaotic knots and wild dynamics. Knot theory and its applications. Chaos Solitons Fractals 9 (1998), no. 4-5, 583--598.
  4. Ibáñez, Raúl; de León, Manuel ; Marrero, Juan C.; Martín de Diego, David ; Padrón, Edith. Some generalizations of Poisson and Jacobi structures. Proceedings of the 1st International Meeting on Geometry and Topology (Braga, 1997), 119--130 (electronic), Cent. Mat. Univ. Minho, Braga, 1998.
  5. Kalashnikov, V. V. Generic integrable Hamiltonian systems on a four-dimensional symplectic manifold. Izv. Math. 62 (1998), no. 2, 261--285.
  6. Médan, Christine. On critical level sets of some two degrees of freedom integrable Hamiltonian systems. Canad. J. Math. 50 (1998), no. 1, 134--151.

1997
  1. Bolsinov, A. V. Fomenko invariants in the theory of integrable Hamiltonian systems. Russian Math. Surveys 52 (1997), no. 5, 997--1015.
  2. Ghrist, Robert W.; Holmes, Philip J.; Sullivan, Michael C. Knots and links in three-dimensional flows. Lecture Notes in Mathematics, 1654. Springer-Verlag, Berlin, 1997. x+208 pp. ISBN: 3-540-62628-X [comment: They used the term "generalized iterated torus knot" that I invented].
  3. Kogan, Mikhail. On completely integrable systems with local torus actions. Ann. Global Anal. Geom. 15 (1997), no. 6, 543--553.
  4. Kruglikov, B. S. On the image in $H\sp 2(Q\sp 3;\bold R)$ of the set of presymplectic forms with a given kernel. (Russian) Mat. Sb. 188 (1997), no. 1, 73--82; translation in Sb. Math. 188 (1997), no. 1, 75--85

1996
  1. Audin, Michèle. Spinning tops. A course on integrable systems. Cambridge Studies in Advanced Mathematics, 51. Cambridge University Press, Cambridge, 1996. viii+139 pp.
  2. Kruglikov, B. S. Monotonicity of a rotation function, and anticonsistent contact structures. Russian Math. Surveys 51 (1996), no. 1, 148--149.
1995
  1. Bleher, Pavel M.; Kosygin, Denis V.; Sinai, Yakov G. Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae. Comm. Math. Phys. 170 (1995), no. 2, 375--403.
  2. Bolsinov, A. V.; Fomenko, A. T. Orbital invariants of integrable Hamiltonian systems. The case of simple systems. Orbital classification of Euler-type systems in the dynamics of a rigid body , Izv. Math.59 (1995), no. 1, 63--100.
  3. Bolsinov, A. V.; Fomenko, A. T. Trajectory equivalence of integrable Hamiltonian systems with two degrees of freedom. Classification theorem. I. (Russian) Mat. Sb. 185 (1994), no. 4,27--80; translation in Russian Acad. Sci. Sb. Math. 81 (1995), no. 2, 421--465; and II, Russian Acad. Sci. Sb. Math. 82 (1995), no. 1, 21--63.
  4. Bolsinov, A. V.; Kozlov, V. V.; Fomenko, A. T. The de Maupertuis principle and geodesic flows on a sphere that arise from integrable cases of the dynamics of a rigid body. Russian Math. Surveys 50 (1995), no. 3, 473--501.
  5. Grossi, Denis. Systèmes intégrables non-dégénérés : invariants symplectiques d'une singularité focus-focus simple. Mémoire DEA (1995).
  6. Hanssmann, Heinz. PhD Thesis (1995).
  7. Lerman, L. M.; Umanskii, Ya. L. Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of $R\sp 2$ in extended neighborhoods of simple singular points. III. Realizations. Sb. Math. 186 (1995), no. 10, 1477--1491 [Comment: their realization result is obvious from the point of view of my decomposition theorem].
  8. Mishachev, K. N. Hamiltonian links in three-dimensional manifolds. Izv. Math. 59 (1995), no. 6, 1193--1205
1994
  1. Kalashnikov, V. V. On the generic character of Bott integrable Hamiltonian systems. (Russian) Mat. Sb. 185 (1994), no. 1, 107--120; translation in Russian Acad. Sci. Sb. Math. 81 (1995), no. 1, 87--99.

1993
  1. Gavrilov, Ljubomir; Ouazzani-Jamil, Mohammed; Caboz, Régis. Bifurcation diagrams and Fomenko's surgery on Liouville tori of the Kolossoff potential $U=\rho+(1/\rho)-k\cos\phi$. Ann. Sci. École Norm. Sup. (4) 26 (1993), no. 5, 545--564.