23 citations · 70 across the 9 of their papers we have counts for
9 papers
Chaotic properties for billiards in circular polygons
Andrew Clarke, Rafael Ramírez-Ros
We study billiards in domains enclosed by circular polygons. These are closed strictly convex curves formed by finitely many circular arcs. We prove the existence of a set in…
Stability of the phase motion in race-track microtons
Yu. A. Kubyshin, O. Larreal, R. Ramírez-Ros +1
We model the phase oscillations of electrons in race-track microtrons by means of an area preserving map with a fixed point at the origin, which represents the synchronous trajecto…
The billiard inside an ellipse deformed by the curvature flow
Josue Damasceno, Mario J. Dias Carneiro, Rafael Ramirez-Ros
The billiard dynamics inside an ellipse is integrable. It has zero topological entropy, four separatrices in the phase space, and a continuous family of convex caustics: the confoc…
On the length and area spectrum of analytic convex domains
Pau Martín, Rafael Ramírez-Ros, Anna Tamarit-Sariol
Area-preserving twist maps have at least two different -periodic orbits and every -periodic orbit has its -periodic action for suitable couples . We est…
On Cayley conditions for billiards inside ellipsoids
Rafael Ramirez-Ros
All the segments (or their continuations) of a billiard trajectory inside an ellipsoid of $\Rset^n$ are tangent to n-1 quadrics of the pencil of confocal quadrics determined by the…
Classification of symmetric periodic trajectories in ellipsoidal billiards
Pablo S. Casas, Rafael Ramírez-Ros
We classify nonsingular symmetric periodic trajectories (SPTs) of billiards inside ellipsoids of R^{n+1} without any symmetry of revolution. SPTs are defined as periodic trajectori…