A partial list of papers/books that cite my work
Last updated: 23/Dec/2002
Nguyen Tien Zung
Preprints
- Bordemann, M.; Makhlouf, A.; Petit, T. Deformation par quantification
et rigidite des algebres enveloppantes, preprint math.RA/0211416.
- Colin de Verdière, Yves. Singular Lagrangian
manifolds and semi-classical analysis, preprint 2001, to appear in
Duke Math. J.
- 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.
- Curras-Bosch, C.; Miranda, E. Symplectic linearization
of singular Lagrangian foliations in M4, preprint (2001), to appear
in Diff. Geom. Appl.
- Dufour, J.-P.; Zhitomirskii, M. Nambu structures
and integrable 1-forms, preprint math.DG/0002167 (2000), to appear in
Let. Math. Phys.
- Ghrist, R.; Komendarczyk, R. Toplological features
of inviscid flows, preprint (2001).
- Martinez Torres, David. Global classification of generic
multi-vector fields of top degree, preprint math.DG/0209374 (2002).
- Rink, Bob. A cantor set of tori with monodromy near a focus-focus
singularity, preprint Utrecht (2001).
- Symington, Margaret. Four dimensions from two in symplectic
topology, preprint math.SG/0210033 (2002).
- Vivolo, Olivier. The mondromy of the Lagrange
Top and the Picard-Lefschetz formula (2001), to appear in J. Geom.
Phys.
- Wade, Aissa. Vinogradov Bracket and Nambu-Dirac Structures
on Lie Algebroids, preprint math.SG/0204310.
2002
- Audin, Michèle. Hamiltonian monodromy via
Picard-Lefschetz theory,
Comm. Math. Phys.
229 (2002),
no. 3,
459--489.
- 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.
- Jovanovic, B. On the integrability of geodesic flows of submersion
metrics,
Lett. Math. Phys.
61 (2002),
no. 1,
29--39.
- Rink, Bob. Direction reversing travelling waves in the Fermi-Pasta-Ulam
chain. nlin.SI/0110015, J. Nonlinear
Science 22 (2002) 479-504.
- 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.
- Vu Ngoc, San. On semi-global invariants for focus-focus
singularities,
Topology, vol 42, number 2, pp. 365--380, 2002
).
- Waalkens, Holger; Dullin, Holger R.
Quantum monodromy in prolate ellipsoidal billiards. Ann. Physics
295 (2002), no. 1, 81--112.
2001
- Cushman, R.; Duistermaat, J. J. Non-Hamiltonian
monodromy. J. Differential Equations 172 (2001), no.
1, 42--58.
- Meinrenken, E. Symplectic geometry. Lecture Notes, University
of Toronto (2001).
- Smith, Ivan. Torus fibrations on symplectic four-manifolds.
Turkish J. Math. 25 (2001), no. 1, 69--95.
- Symington, Margaret. Generalized rational symplectic
blowdown, Algebr. Geom. Topol. 1 (2001) 503-518.
- Zhilinskii, B.I.Qualitative features of quantum finie particle
systems, Proceedings of Andronov memorial conference, Frontiers of Nonlinear
Science, Nozhnii Novgorod (2001).
2000
- 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.
- 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.
- Cushman, R. H.; Sadovskií, D. A. Monodromy
in the hydrogen atom in crossed fields. Phys. D 142
(2000), no. 1-2, 166--196.
- Dufour, Jean-Paul. Singularities of Poisson and Nambu
structures. Poisson geometry (Warsaw, 1998), 61--68, Banach
Center Publ., 51, Polish Acad. Sci., Warsaw, 2000.
- Etnyre, John; Ghrist, Robert. Contact topology
and hydrodynamics. I. Beltrami fields and the Seifert conjecture.
Nonlinearity 13 (2000), no. 2, 441--458.
- Grabowski, J.; Marmo, G. On Filippov algebroids
and multiplicative Nambu-Poisson structures. Differential Geom.
Appl. 12 (2000), no. 1, 35--50.
- 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].
- 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.
- Vaisman, Izu. Nambu-Lie groups. J. Lie Theory
10 (2000), no. 1, 181--194.
- 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.
- Wade, Aïssa. Conformal Dirac structures. Lett.
Math. Phys. 53 (2000), no. 4, 331--348.
1999
- 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.
- 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.
- 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.
- Grabowski, J.; Marmo, G. Remarks on Nambu-Poisson
and Nambu-Jacobi brackets. J. Phys. A 32 (1999), no.
23, 4239--4247.
- Kudryavtseva, E. A. Realization of smooth functions
on surfaces as height functions. Sb. Math. 190 (1999), no.
3-4, 349--405.
- Médan, Christine. Degenerate invariant manifolds
of some completely integrable systems. Math. Z. 232
(1999), no. 4, 665--689.
- Nakanishi, N. A survey of Nambu-Poisson geometry.
Towards 100 years after Sophus Lie (Kazan, 1998). Lobachevskii
J. Math. 4 (1999), 5--11 (electronic).
- Vaisman, Izu. A survey on Nambu-Poisson brackets. Acta
Math. Univ. Comenian. (N.S.) 68 (1999), no. 2,
213--241.
- Vu Ngoc, San. Quantum monodromy in integrable
systems. Comm. Math. Phys. 203 (1999),
no. 2, 465--479.
1998
- 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.
- Brailov, Yu. A. Algebraic aspects of classification
of singularities in Hamiltonian systems. Regul. Chaotic Dyn.
4 (1999), no. 3, 30--34.
- Ghrist, Robert W. Chaotic knots and wild dynamics.
Knot theory and its applications. Chaos Solitons Fractals
9 (1998), no. 4-5, 583--598.
- 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.
- Kalashnikov, V. V. Generic integrable Hamiltonian
systems on a four-dimensional symplectic manifold. Izv. Math.
62 (1998), no. 2, 261--285.
- 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
- Bolsinov, A. V. Fomenko invariants in the theory
of integrable Hamiltonian systems. Russian Math. Surveys
52 (1997), no. 5, 997--1015.
- 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].
- Kogan, Mikhail. On completely integrable systems
with local torus actions. Ann. Global Anal. Geom. 15 (1997),
no. 6, 543--553.
- 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
- Audin, Michèle. Spinning tops. A course on
integrable systems. Cambridge Studies in Advanced Mathematics,
51. Cambridge University Press, Cambridge, 1996. viii+139
pp.
- Kruglikov, B. S. Monotonicity of a rotation function,
and anticonsistent contact structures. Russian Math. Surveys
51 (1996), no. 1, 148--149.
1995
- 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.
- 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.
- 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.
- 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.
- Grossi, Denis. Systèmes intégrables
non-dégénérés : invariants symplectiques d'une
singularité focus-focus simple. Mémoire DEA
(1995).
- Hanssmann, Heinz. PhD Thesis (1995).
- 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].
- Mishachev, K. N. Hamiltonian links in three-dimensional
manifolds. Izv. Math. 59 (1995), no. 6, 1193--1205
1994
- 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
- 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.