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Positive exponent in families with flat critical point. (English) Zbl 0966.37011
The author considers a certain full unimodal family of \(C^\infty\) flat top functions with a flat critical point (all derivatives at this point are zero). The functions considered are flat top versions of the standard quadratic family. The author investigates the invariant probability measures, existence of periodic attractors for the family and sets of positive measure in the parameter space that relate to chaotic behavior of the maps.

MSC:
37E05 Dynamical systems involving maps of the interval
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37A05 Dynamical aspects of measure-preserving transformations
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