Rafael Ramírez-Ros (Research)
Fields of interest
- Dynamical systems:
Billiards, spliting of separatrices, breaking of invariant curves.
- Numerical methods:
Computation of invariant manifolds,
multiple-precision arithmetic.
Courses
Preprints
Papers
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The frequency map for billiards inside ellipsoids
Pablo S. Casas,
Rafael Ramírez-Ros
SIAM J. Appl. Dyn. Syst.
10:278-324, 2011
MR2788926
Abstract,
PDF.
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Separatrix splitting for 3D volume-preserving maps
Héctor E. Lomelí,
Rafael Ramírez-Ros
SIAM J. Appl. Dyn. Syst.,
7:1527-1557, 2008
MR 2009k:37044
Abstract,
PDF.
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Canonical Melnikov theory for diffeomorphisms
Héctor E. Lomelí,
James D. Meiss,
Rafael Ramírez-Ros
Nonlinearity,
21:485-508, 2008
MR 2009e:37014
Abstract,
PDF.
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Break-up of resonant invariant curves in billiards and dual billiards
associated to perturbed circular tables
Rafael Ramírez-Ros
Physica D,
214:78-87, 2006.
MR 2006i:37120
Abstract,
PDF.
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Exponentially small separatrix splittings and almost invisible
homoclinic bifurcations in some billiard tables
Rafael Ramírez-Ros
Physica D,
210:149-179, 2005.
MR 2006k:37165
Abstract,
PDF.
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Persistence of homoclinic orbits for billiards and twist maps
Sergey Bolotin,
Amadeu Delshams,
Rafael Ramírez-Ros
Nonlinearity,
17:1153-1177, 2004.
MR 2005d:37126
Abstract,
PDF.
- Homoclinic billiard orbits inside symmetrically perturbed
ellipsoids
Amadeu Delshams,
Yuri Fedorov,
Rafael Ramírez-Ros
Nonlinearity,
14:1141-1195, 2001.
MR 2002h:37120
Abstract,
PDF.
- 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,
PDF.
- 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,
PDF.
- Melnikov potential for exact symplectic maps
Amadeu Delshams,
Rafael Ramírez-Ros
Comm. Math. Phys.,
190(1):213-245, 1997.
MR 99f:58154
Abstract,
PDF.
- Effective Reducibility of Quasiperiodic Linear Equations
Close to Constant Coefficients
Àngel Jorba,
Rafael Ramírez-Ros,
Jordi Villanueva
SIAM Journal on Mathematical Analysis,
28(1):178-188, 1997.
MR 97j:34008
Abstract,
PDF.
- Poincaré-Melnikov-Arnold method for analytic planar maps
Amadeu Delshams,
Rafael Ramírez-Ros
Nonlinearity,
9:1-26, 1996.
MR 97b:58125
Abstract,
PDF.
Proceedings
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Existence and non-existence of (convex) caustics
Rafael Ramírez-Ros
Arbeitsgemeinschaft mit aktuellen Thema: Mathematical Billiards,
3 pages, Mathematiches Forschungsinstitut Oberwolfach (MFO), Oberwolfach, 2010.
This is the published version:
Abstract,
PDF.
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Singular phenomena for convex billiard tables
Rafael Ramírez-Ros
XVIII CEDYA/VIII CMA, (Tarragona, 2003),
8 pages, Univ. Rovira i Virgili, Tarragona, 2003.
This is the published version:
Abstract,
PostScript.
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Bi-asymptotic billiard orbits inside perturbed ellipsoids
Sergey Bolotin,
Amadeu Delshams,
Yuri Fedorov,
Rafael Ramírez-Ros
L. Lerman and L. Shilnikov, editors,
Proceedings of the International Conference on Progress in
Nonlinear Science (Volume I) ,
pp. 48-62, Nizhny Novgorod, Russia, 2002.
MR 1 965 024
This is the preprint version:
Abstract,
PostScript,
PDF.
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Trayectorias periódicas de billares en circunferencias
perturbadas
Rafael Ramírez-Ros
XVII CEDYA/VII CMA, (Salamanca, 2001),
8 pages, Univ. Salamanca, Salamanca, 2001.
This is the published version:
Abstract,
PostScript,
PDF.
- 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.
MR 1 870 265
This is the preprint version:
Abstract,
PostScript,
PDF.
- 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
This is the preprint version:
Abstract,
PostScript,
PDF.
- 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
This is the preprint version:
Abstract,
PostScript,
PDF.
- 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
This is the preprint version:
Abstract,
PostScript,
PDF.
- 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.
This is the published version:
Abstract,
PostScript,
zipped PostScript.
- 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
This is the published version:
Abstract,
PostScript.
http://www.ma1.upc.edu/~rafael/research.html