Regularity of the spectrum for expanding maps
arXiv:1711.05647
Abstract
In this short note, we propose to extend differentiability (with respect to a multidimensional parameter) of a normalized eigenfunction associated to the simple, dominating eigenvalue of the weighted transfer operator for a uniformly expanding map, to the whole discrete spectrum. We do so by studying directly the regularity (with respect to the parameter) of the resolvent operator, applying a general regularity result for fixed points of maps having loss of regularity.
This is the second version: an error in the main argument was found in the previous version, which now stands corrected. The author would like to thank Hans Henrik Rugh for his advice on the matter