Existence of additional tiny basins of attraction in the forced damped pendulum example

Ascertain whether additional basins of attraction exist for the time-2π Poincaré return map of the forced damped pendulum at parameters γ=0.2 and ρ=2 beyond the two numerically observed basins associated with the attracting fixed points.

Background

The analysis of the forced damped pendulum is numerical. The authors display two basins of attraction corresponding to two attracting fixed points, along with three chaotic saddles. Because the results are numerical, they explicitly acknowledge uncertainty about the possible presence of additional very small basins not detected by the numerical grid.

Determining whether such basins exist is a concrete question about the completeness of the basin structure at the stated parameter values.