Smooth deformations of piecewise expanding unimodal maps

Abstract

In the space of C^k piecewise expanding unimodal maps, k>=1, we characterize the C^1 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.

19 pages. Few misprints fixed. Minor improvements

References in corpus (2)

• Linear response formula for piecewise expanding unimodal maps
• On the susceptibility function of piecewise expanding interval maps

Cited by in corpus (7)

• Linear response formula for piecewise expanding unimodal maps
• Linear response, or else
• Central limit theorem for the modulus of continuity of averages of observables on transversal families of piecewise expanding unimodal maps
• On the fractional susceptibility function of piecewise expanding maps
• Central limit theorem for generalized Weierstrass functions
• Regularity of absolutely continuous invariant measures for piecewise expanding unimodal maps
• Alternative proofs of linear response for piecewise expanding unimodal maps