Rafael Ramírez-Ros (Research)
Fields of interest
- Dynamical systems:
Billiards, twist maps, Hamiltonian systems,
integrable dynamics, chaotic dynamics,
perturbation methods, bifurcations, exponentially small phenomena
- Numerical methods:
Computation of periodic orbits and invariant manifolds,
analysis of bifurcations, multiple-precision arithmetic
Publications
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High-order persistence of resonant caustics in
perturbed circular billiards
Comlan Edmond Koudjinan, Rafael Ramírez-Ros
Ergodic Theory and Dynamical Systems 46: 514–542, 2026
PDF (revised preprint version),
arXiv 2503.07488
-
Chaotic properties of billiards in circular polygons
Andrew Clarke, Rafael Ramírez-Ros
Communications in Mathematical Physics 405: 263, 2024
PDF (revised preprint version),
arXiv 2309.09892
-
Stability of the phase motion in race-track microtons
Yuri A. Kubyshin, Oswaldo Larreal, Rafael Ramírez-Ros,
Tere M. Seara
Physica D
349:12–26, 2017
-
The billiard inside an ellipse deformed by the curvature flow
Josué Damasceno, Mario J. Dias Carneiro, Rafael Ramírez-Ros
Proceedings of the American Mathematical
Society
145:705–719, 2017
-
Exponentially small asymptotic formulas for the length spectrum
in some billiard tables
Pau Martín, Rafael Ramírez-Ros, Anna Tamarit-Sariol
Experimental Mathematics
25:416–440, 2016
-
On the length and area spectrum of analytic convex domains
Pau Martín, Rafael Ramírez-Ros, Anna Tamarit-Sariol
Nonlinearity
29:198–231, 2016
-
On Cayley conditions for billiards inside ellipsoids
Rafael Ramírez-Ros
Nonlinearity
27:1003–1028, 2014
-
Nonpersistence of resonant caustics in perturbed elliptic billiards
Sônia Pinto-de-Carvalho, Rafael Ramírez-Ros
Ergodic Theory and Dynamical Systems
33:1876–1890, 2013
-
Classification of symmetric periodic trajectories in ellipsoidal billiards
Pablo S. Casas, Rafael Ramírez-Ros
CHAOS
22:026110 (24 pages), 2012
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Billiards with a given number of (k,n)-orbits
Sônia Pinto-de-Carvalho, Rafael Ramírez-Ros
CHAOS
22:026109 (6 pages), 2012
-
The frequency map for billiards inside ellipsoids
Pablo S. Casas, Rafael Ramírez-Ros
SIAM Journal on Applied Dynamical
Systems
10:278–324, 2011
-
Separatrix splitting for 3D volume-preserving maps
Héctor E. Lomelí,
Rafael Ramírez-Ros
SIAM Journal on Applied Dynamical
Systems
7:1527–1557, 2008
-
Canonical Melnikov theory for diffeomorphisms
Héctor E. Lomelí,
James D. Meiss,
Rafael Ramírez-Ros
Nonlinearity
21:485–508, 2008
-
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
-
Exponentially small separatrix splittings and almost invisible
homoclinic bifurcations in some billiard tables
Rafael Ramírez-Ros
Physica D
210:149–179, 2005
-
Persistence of homoclinic orbits for billiards and twist maps
Sergey Bolotin,
Amadeu Delshams,
Rafael Ramírez-Ros
Nonlinearity
17:1153–1177, 2004
- Homoclinic billiard orbits inside symmetrically perturbed
ellipsoids
Amadeu Delshams,
Yuri Fedorov,
Rafael Ramírez-Ros
Nonlinearity
14:1141–1195, 2001
- Singular separatrix splitting and Melnikov method:
An experimental study
Amadeu Delshams,
Rafael Ramírez-Ros
Experimental Mathematics
8:29–48, 1999
- Exponentially small splitting of separatrices for perturbed
integrable standard-like maps
Amadeu Delshams,
Rafael Ramírez-Ros
Journal of Nonlinear Science
8:317–352, 1998
- Melnikov potential for exact symplectic maps
Amadeu Delshams,
Rafael Ramírez-Ros
Communications in Mathematical Physics
190:213–245, 1997
- Effective Reducibility of Quasiperiodic Linear Equations
Close to Constant Coefficients
Àngel Jorba,
Rafael Ramírez-Ros,
Jordi Villanueva
SIAM Journal on Mathematical Analysis
28:178–188, 1997
- Poincaré-Melnikov-Arnold method for analytic planar maps
Amadeu Delshams,
Rafael Ramírez-Ros
Nonlinearity
9:1–26, 1996