Smooth Deformations of Piecewise Expanding Unimodal Maps
نویسندگان
چکیده
In the space of C piecewise expanding unimodal maps, k ≥ 2, we characterize the C smooth families of maps where the topological dynamics does not change (the “smooth deformations”) as the families tangent to a continuous distribution of codimension-one subspaces (the “horizontal” directions) in that space. Furthermore such codimension-one subspaces are defined as the kernels of an explicit class of linear functionals. As a consequence we show the existence of C deformations tangent to every given C horizontal direction, for k ≥ 2.
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