Amadeu Delshams
- Position: Professor of Applied Mathematics
- Research interests: Dynamical systems:
Effective estability of Hamiltonian and reversible systems,
whiskered tori, splitting of separatrices, Arnold diffusion.
Preprints
- Homoclinic billiard orbits inside symmetrically perturbed
ellipsoids
Amadeu Delshams,
Yuri Fedorov,
Rafael Ramírez-Ros
Abstract (ASCII file),
zipped PostScript (798 Kb), 63 pages.
- Unbounded growth of energy in periodic perturbations of
geodesic flows of the torus
Amadeu Delshams,
Rafael de la Llave,
Tere M. Seara
J. Delgado, E.A. Lacomba, E. Pérez-Chavela, J. Llibre, editors,
Hamiltonian systems and Celestial mechanics (HAMSYS-98),
volume 6 of
World Scientific Monograph Series in Mathematics,
World Sci. Publishing, 2000.
Abstract (ASCII file),
PostScript (330 Kb),
zipped version (102 Kb).
- Splitting and Melnikov potentials in Hamiltonian systems
Amadeu Delshams,
Pere Gutiérrez
J. Delgado, E.A. Lacomba, E. Pérez-Chavela, J. Llibre, editors,
Hamiltonian systems and Celestial mechanics (HAMSYS-98),
volume 6 of
World Scientific Monograph Series in Mathematics,
World Sci. Publishing, 2000.
Abstract (ASCII file),
PostScript (277 Kb),
zipped version (106 Kb).
Recent publications
- Homoclinic orbits to invariant tori in Hamiltonian systems
Amadeu Delshams,
Pere Gutiérrez
C.K.R.T. Jones, A. Khibnik, editors,
Multiple-Time-Scale Dynamical Systems, pp. 1-28,
volume 122 of
IMA Vol. Math. Appl.,
Springer-Verlag, Berlin, 2000.
Abstract (ASCII file),
PostScript (311 Kb),
zipped version (119 Kb).
- Singular separatrix splitting and the Poincaré-Melnikov
method for area preserving maps
Amadeu Delshams,
Rafael Ramírez-Ros
B. Fiedler, K. Gröger, J. Sprekels, editors,
EQUADIFF 99, pp. 941-946,
World Sci. Publishing, 2000.
Abstract (ASCII file),
PostScript (153 Kb),
Pdf version (163 Kb),
zipped version (177 Kb).
- Splitting potential and Poincaré-Melnikov method for whiskered
tori in Hamiltonian Systems
Amadeu Delshams,
Pere Gutiérrez
J. Nonlinear Sci.,
10(4):433-476, 2000.
CMP 1766491
Abstract (ASCII file),
LaTeX (139 Kb),
PostScript (481 Kb),
zipped version (221 Kb).
- KAM theory and a partial justification of Greene's criterion for
non-twist maps
Amadeu Delshams,
Rafael de la Llave
SIAM J. Math. Anal.,
31(6):1235-1269, 2000.
CMP 1766561
Abstract (ASCII file),
TeX (141 Kb),
PostScript (393 Kb),
zipped version (190 Kb).
- A geometric approach to the existence of orbits with unbounded energy
in generic periodic perturbations by a potential of generic geodesic
flows of T2
Amadeu Delshams,
Rafael de la Llave,
Tere M. Seara
Comm. Math. Phys.,
209(2):353-392, 2000.
MR 2001a:37086
Abstract (ASCII file),
LaTeX (279 Kb),
PostScript (579 Kb),
zipped version (258 Kb).
- Singular separatrix splitting and Melnikov method:
An experimental study
Amadeu Delshams,
Rafael Ramírez-Ros
Experiment. Math.,
8(1):29-48, 1999.
MR 2000c:37094
Abstract (ASCII file),
PostScript (775 Kb),
zipped version (304 Kb).
- Splitting of separatrices in Hamiltonian systems
and symplectic maps
Amadeu Delshams,
Tere M. Seara,
Rafael Ramírez-Ros
C. Simó, editor,
Hamiltonian Systems with Three or More Degrees of Freedom,
volume 533 of
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.,
pp. 39-54. Kluwer, Dordrecht, 1999.
MR 2000j:37075
Abstract (ASCII file),
PostScript (262 Kb),
zipped version (102 Kb).
- Splitting of separatrices for (fast) quasiperiodic forcing
Amadeu Delshams,
Vassili Gelfreich,
Àngel Jorba,
Tere M. Seara
C. Simó, editor,
Hamiltonian Systems with Three or More Degrees of Freedom,
volume 533 of
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.,
pp. 367-371. Kluwer, Dordrecht, 1999.
CMP 1720914
Abstract (ASCII file),
PostScript (108 Kb),
zipped version (42 Kb).
- Exponentially small estimates for KAM theorem
near an elliptic equilibrium point
Amadeu Delshams,
Pere Gutiérrez
C. Simó, editor,
Hamiltonian Systems with Three or More Degrees of Freedom,
volume 533 of
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.,
pp. 386-390. Kluwer, Dordrecht, 1999.
MR 2000g:37087
Abstract (ASCII file),
PostScript (84 Kb),
zipped version (35 Kb).
- Effective stability in reversible systems
Amadeu Delshams,
José Tomás Lázaro
C. Simó, editor,
Hamiltonian Systems with Three or More Degrees of Freedom,
volume 533 of
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.,
pp. 453-457. Kluwer, Dordrecht, 1999.
MR 2000g:37088
Abstract (ASCII file),
PostScript (96 Kb),
zipped version (39 Kb).
- Psi-series, singularities of solutions and integrability of
polynomial systems
Arnau Mir,
Amadeu Delshams
C. Simó, editor,
Hamiltonian Systems with Three or More Degrees of Freedom,
volume 533 of
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.,
pp. 504-508. Kluwer, Dordrecht, 1999.
CMP 1720937
Abstract (ASCII file),
PostScript (71 Kb),
zipped version (30 Kb).
- Poincaré-Melnikov-Arnold method for twist maps
Amadeu Delshams,
Rafael Ramírez-Ros
C. Simó, editor,
Hamiltonian Systems with Three or More Degrees of Freedom,
volume 533 of
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.,
pp. 533-537. Kluwer, Dordrecht, 1999.
MR 2000g:37101
Abstract (ASCII file),
PostScript (125 Kb),
zipped version (54 Kb).
- Exponentially small splitting of separatrices for perturbed
integrable standard-like maps
Amadeu Delshams,
Rafael Ramírez-Ros
J. Nonlinear Sci.,
8(3):317-352, 1998.
MR 99f:58177
Abstract (ASCII file),
PostScript (644 Kb),
zipped version (229 Kb).
- Singular splitting of separatrices for the perturbed McMillan map
Amadeu Delshams,
Rafael Ramírez-Ros
XV Congress on Differential Equations and Applications/V Congress
on Applied Mathematics, Vol. I, II (Vigo, 1997),
pp. 243--248. Univ. Vigo, Vigo, 1998.
MR 99e:58156
Abstract (ASCII file),
PostScript (127 Kb),
zipped version (52 Kb).
- Homoclinic orbits of twist maps and billiards
Amadeu Delshams,
Rafael Ramírez-Ros
D. Bambusi and G. Gaeta, editors,
Symmetry and Perturbation Theory, Quaderno GNFM, 54,
pp. 46-86. Firenze, Italy, 1998.
Abstract (ASCII file),
PostScript (644 Kb),
zipped version (230 Kb).
- Melnikov potential for exact symplectic maps
Amadeu Delshams,
Rafael Ramírez-Ros
Comm. Math. Phys.,
190(1):213-245, 1997.
MR 99f:58154
Abstract (ASCII file),
PostScript (565 Kb),
zipped version (202 Kb).
- Splitting of separatrices in Hamiltonian systems with one
and a half degrees of freedom
Amadeu Delshams,
Tere M. Seara
Math. Phys. Electron. J.,
3(1): 1-40, 1997.
MR 98k:58197
Abstract (ASCII file),
PostScript (485 Kb),
zipped version (178 Kb).
- Exponentially small splitting of separatrices under fast
quasiperiodic forcing
Amadeu Delshams,
Vassili Gelfreich,
Àngel Jorba,
Tere M. Seara
Comm. Math. Phys.,
189(1): 35-71, 1997.
MR 98j:34087
Abstract (ASCII file),
PostScript (393 Kb),
zipped version (140 Kb).
- Psi-series of quadratic vector fields on the plane
Amadeu Delshams,
Arnau Mir
Publ. Mat.,
41(1):101-125, 1997.
MR 98h:34008
Abstract (ASCII file),
PostScript (272 Kb),
LaTeX 2.09 (81 Kb),
zipped version (129 Kb).
- Lower and upper bounds for the splitting of separatrices of the
pendulum under a fast quasiperiodic forcing
Amadeu Delshams,
Vassili Gelfreich,
Àngel Jorba,
Tere M. Seara
Electron. Res. Announc. Amer. Math. Soc.,
3:1-10, 1997.
MR 98a:58135
Abstract (ASCII file),
PostScript (127 Kb),
zipped version (50 Kb).
- Estimates on invariant tori near an elliptic equilibrium point
of a Hamiltonian system
Amadeu Delshams,
Pere Gutiérrez
J. Differential Equations,
131:277-303, 1996.
MR 97j:58133
Abstract (ASCII file),
PostScript (243 Kb),
zipped version (94 Kb).
- Effective stability and KAM theory
Amadeu Delshams,
Pere Gutiérrez
J. Differential Equations,
128:415-490, 1996.
MR 97e:58202
Abstract (ASCII file),
PostScript (604 Kb),
zipped version (214 Kb).
- Poincaré-Melnikov-Arnold method for analytic planar maps
Amadeu Delshams,
Rafael Ramírez-Ros
Nonlinearity,
9:1-26, 1996.
MR 97b:58125
Abstract (ASCII file),
PostScript (386 Kb),
zipped version (141 Kb).
- On Birkhoff's conjecture about convex billiards
Amadeu Delshams,
Rafael Ramírez-Ros
M. Sofonea and J.-N. Corvellec, editors,
Proceedings of the 2nd Catalan Days on Applied Mathematics
(Odeillo, 1995), Collect. Études, pp. 85-94.
Presses Univ. de Perpignan, Perpignan, 1995.
MR 98m:58117
Abstract (ASCII file),
PostScript (142 Kb),
zipped version (57 Kb).
http://www.ma1.upc.edu/~amadeu/
Last modified Tuesday, September 4, 2001
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