An interval map with a spectral gap on Lipschitz functions, but not on bounded variation functions

2008/09/03 by Sébastien Gouëzel, Sebastien Gouezel, Gouezel, Sebastien
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.0809.0658

4 pages

arxiv created 2008/09/03 · openalex publication_date 2008/09/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a uniformly expanding map of the interval, preserving Lebesgue measure, such that the corresponding transfer operator admits a spectral gap on the space of Lipschitz functions, but does not act continuously on the space of bounded variation functions.

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