Smooth deformations of piecewise expanding unimodal maps

Daniel Smania | Baladi, Viviane

Keywords: deformation | piecewise expanding unimodal map

In the space of C^k piecewise expanding unimodal maps, k >= 2, we characterize the C2 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^{k-1+Lip} deformations tangent to every given C^k horizontal direction, for k>=2.

Anexos:

• smooth.pdf