Partially nearly riddled basins in systems with chaotic saddle
The author deals with the basin of attraction, that is, the basin which contains open sets but with a special property, can occur in coupled systems with at least two co-existing attractors. This pecularity is caused by the existence of a region in the phase space in which small open sets which belong to the basins of different co-existing attractors are intermingled. These sets are open as preimages of the large open sets located in the neighborhoods of the attractors (for example its immediate basins), but on the other hand so small that in the relatively small (in comparison with the noise level) neighborhood of any point in them there are points which belong to the basin of different attractor.
scientific article; zbMATH DE number 1755340