Quantify duration, stability, and sustaining conditions of stickiness episodes

Determine the characteristic duration of stickiness episodes, establish finite-time dynamical stability properties of sticky chaotic trajectories, and identify system conditions that sustain or enhance stickiness episodes in mixed-type Hamiltonian phase spaces, with particular relevance to the time-dependent potential well map defined in the Model section.

Background

The paper introduces an ensemble recurrence analysis (ERA) to detect highly recurrent chaotic trajectories (stickiness) in a time-dependent potential well map. These sticky trajectories, though originating from low energy, can display prolonged high-energy plateaus due to transient trapping near regular structures.

While ERA successfully identifies such orbits and links high recurrence rates to stickiness, the authors explicitly flag unresolved aspects of the stickiness phenomenon itself: how long sticky episodes last, how stable they are over finite times, and under what conditions these events are sustained or enhanced. Addressing these points would systematize the understanding of stickiness beyond qualitative observation and help explain when and why sustained high-energy episodes occur.