Smooth Livšic regularity for piecewise expanding maps
Smooth Livšic regularity for piecewise expanding maps
We consider the regularity of measurable solutions $\chi$ to the cohomological equation \[ \phi = \chi \circ T -\chi , \] where $(T,X,\mu )$ is a dynamical system and $\phi \colon X\rightarrow \mathbb {R}$ is a $C^k$ smooth real-valued cocycle in the setting in which $T \colon X\rightarrow X$ is …