Relativistic chaotic scattering: Unveiling scaling laws for trapped trajectories.

In this paper we study different types of phase space structures which appear in the context of relativistic chaotic scattering. By using the relativistic version of the Hénon-Heiles Hamiltonian, we numerically study the topology of different kind of exit basins and compare it with the case of low velocities in which the Newtonian version of the system is valid. Specifically, we numerically study the escapes in the phase space, in the energy plane, and in the β plane, which richly characterize the dynamics of the system.

Unbounded dynamics in dissipative flows: Rössler model.

Transient chaos and unbounded dynamics are two outstanding phenomena that dominate in chaotic systems with large regions of positive and negative divergences. Here, we investigate the mechanism that leads the unbounded dynamics to be the dominant behavior in a dissipative flow. We describe in detail the particular case of boundary crisis related to the generation of unbounded dynamics.

Topological changes in periodicity hubs of dissipative systems.

We reveal the existence of a new codimension-1 curve that involves a topological change in the structure of the chaotic invariant sets (attractors and saddles) in generic three-dimensional dissipative systems with Shilnikov saddle foci. This curve is related to the spiral-like structures of periodicity hubs that appear in the biparameter phase plane. We show how this curve configures the spiral structure (via the doubly superstable points) originated by the existence of Shilnikov homoclinics and how it separates two regions with different kinds of chaotic attractors or chaotic saddles.

Global organization of spiral structures in biparameter space of dissipative systems with Shilnikov saddle-foci.

We reveal and give a theoretical explanation for spiral-like structures of periodicity hubs in the biparameter space of a generic dissipative system. We show that organizing centers for "shrimp"-shaped connection regions in the spiral structure are due to the existence of Shilnikov homoclinics near a codimension-2 bifurcation of saddle-foci.