Jumping stable manifolds for dissipative maps of the plane (Q1262589)

An essential assumption of the authors is that basin boundaries arise `typically' from stable manifolds of saddle points. Other separatrices are ignored. The `discontinuity' argument is inspired by low accuracy numerical computations. A numerical study of a particular \({\mathbb{C}}\to {\mathbb{C}}\) map, due to Ikeda, is used as confirming evidence. For \({\mathbb{C}}\to {\mathbb{C}}\) maps it was already known to Julia (70 years ago) that basin boundaries can have an extremely complicated structure, not necessarily related to saddle-point manifolds. Other non-`typical' cases can be found in books, for example [in the reviewer and \textit{C. Mira}: Recurrences and discrete dynamical systems (Lect. Notes Math. 809, 1980; Zbl 0449.58003)].