Tunable Fermi acceleration in a nondissipative driven magnetic billiard.

We study the effect of a constant magnetic field on the dynamics of a system that may present Fermi acceleration (FA). The model in consideration is the nondissipative annular billiard with breathing boundaries. There is a field threshold, from which the mechanism of FA can be deactivated. The presence of the magnetic field curves the particle trajectories and for some combinations of the parameters FA is totally, and nontrivially, suppressed without considering any kind of dissipation.

Secondary nontwist phenomena in area-preserving maps.

Phenomena as reconnection scenarios, periodic-orbit collisions, and primary shearless tori have been recognized as features of nontwist maps. Recently, these phenomena and secondary shearless tori were analytically predicted for generic maps in the neighborhood of the tripling bifurcation of an elliptic fixed point. In this paper, we apply a numerical procedure to find internal rotation number profiles that highlight the creation of periodic orbits within islands of stability by a saddle-center bifurcation that emerges out a secondary shearless torus. In addition to the analytical predictions, our numerical procedure applied to the twist and nontwist standard maps reveals that the atypical secondary shearless torus occurs not only near a tripling bifurcation of the fixed point but also near a quadrupling bifurcation.

Dissipation as a mechanism of energy gain.

Some properties of the annular billiard under the presence of weak dissipation are studied. We show, in a dissipative system, that the average energy of a particle acquires higher values than its average energy of the conservative case. The creation of attractors, associated with a chaotic dynamics in the conservative regime, both in appropriated regions of the phase space, constitute a generic mechanism to increase the average energy of dynamical systems.