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Regularity of the spectrum for expanding maps

2017/11/15 by Julien Sedro, Sedro, Julien
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #math.DS #math.FA

paper · pdf · doi:10.48550/arxiv.1711.05647

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

openalex publication_date 2017/11/15 · arxiv created 2018/10/11 · arxiv updated 2018/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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