Regularity of the spectrum for expanding maps
Dynamical Systems
2018-10-12 v2 Functional Analysis
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.
Cite
@article{arxiv.1711.05647,
title = {Regularity of the spectrum for expanding maps},
author = {Julien Sedro},
journal= {arXiv preprint arXiv:1711.05647},
year = {2018}
}
Comments
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