A mechanism for stickness, dealing with extreme events

TL;DR

This paper investigates how hyperbolic and non-hyperbolic regions near resonant islands influence stickiness in conservative systems, revealing ways to manipulate extreme events and system transport by monitoring small phase space areas.

Contribution

It identifies the role of phase space structures in stickiness and demonstrates control of extreme events by monitoring tiny phase space regions.

Findings

Non hyperbolic regions prevent trajectories from visiting island edges.

Tiny channels near hyperbolic fixed points enable injection into island vicinity.

Monitoring small phase space portions can eliminate long-term recurrences.

Abstract

In this letter we study how hyperbolic and non hyperbolic regions in the neighborhood of a resonant island perform a important role allowing or forbidding stickiness phenomenon around islands in conservative systems. The vicinity of the island is composed by non hyperbolic areas that almost prevent the trajectory to visit the island edge. For some specific parameters there are tiny channels embedded in the non hyperbolic area that are associated to hyperbolic fixed points present in the neighborhood of the islands. Such channels allow the trajectory to be injected in the inner portion of the vicinity. When the trajectory crosses the barrier imposed by the non hyperbolic regions, it spends a long time to abandon the surrounding of the island, since the barrier also prevents the trajectory to scape from the neighborhood of the island. In this scenario the non hyperbolic structures are the responsible for the stickiness phenomena, and more than that, the strength of the sticky effect. We reveal that those properties of the phase space allow us to manipulate the existence of extreme events (and the transport associated to it) responsible for the non equilibrium fluctuation of the system. In fact we demonstrate that monitoring very small portions of the phase space (namely $\approx 4\times 10^{-4}$ \% of it) it is possible to generate a completely diffusive system eliminating long time recurrences that result from the stickiness phenomenon.