Recurrence in two degrees of freedom Hamiltonian flows

Stickiness in mixed Hamiltonian systems causes chaotic trajectories to remain temporarily trapped near regular structures, making it difficult to distinguish regular, weakly chaotic, and strongly chaotic motion over finite times. We show that the recurrence time entropy (RTE), previously used in discrete maps, also characterizes weak chaos in Hamiltonian flows. In the H\'enon-Heiles system, the RTE reproduces the phase space structures identified by the largest Lyapunov exponent: low values in regular islands, higher values in chaotic regions, and intermediate values in sticky layers. The proportion of chaotic trajectories identified by the RTE is consistent with that obtained from the smaller alignment index (SALI). The finite-time RTE series identify low-entropy episodes near regular islands, associated with temporary trapping. The duration of these episodes displays algebraic decay, while high-entropy episodes display exponential statistics. These results establish the RTE as an effective diagnostic of weak chaos and stickiness in Hamiltonian flows.