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Basin boundary metamorphoses: Changes in accessible boundary orbits. (English) Zbl 0613.58018
The authors investigate what they call ”basin boundary metamorphoses”. As is well known, the boundary of the basin of attraction of a fixed or periodic point for a smooth map is often a fractal. Sometimes these basin boundaries undergo sudden changes as parameters are changed. For example, basin boundaries may change in size or shape at particular parameter values. This has been observed in many maps, including the often-studied Hénon map.
The authors propose one mechanism for these transitions. Often, there are infinitely many unstable periodic points in a basin boundary. However, only one is ”usually” accessible. The authors suggest that when this accessible point changes, the basin boundary undergoes a metamorphosis.
Reviewer: R.Devaney

MSC:
37B99 Topological dynamics
37N99 Applications of dynamical systems
28A75 Length, area, volume, other geometric measure theory
26A18 Iteration of real functions in one variable
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