The Newhouse set has a positive Hausdorff dimension
As observed first by \textit{S. E. Newhouse} [Topology 13, 9-18 (1974; Zbl 0275.58016), Publ. Math., Inst. Hautes Etud. Sci. 50, 101-152 (1979; Zbl 0445.58022)] an infinite number of periodic attractors may coexist in a bounded region of a multidimensional dynamical system. The author constructs a one-parameter family of planar diffeomorphisms which shows this phenomenon for a set of parameters with positive Hausdorff dimension.
scientific article; zbMATH DE number 4163773