Eigenfunctions for smooth expanding circle maps

Abstract

We construct a real-analytic circle map for which the corresponding Perron-Frobenius operator has a real-analytic eigenfunction with an eigenvalue outside the essential spectral radius when acting upon $C^1$-functions.

10 pages, 2 figures

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• Generic non-trivial resonances for Anosov diffeomorphisms
• Discontinuities cause essential spectrum
• A spectral gap for transer operators of piecewise expanding maps
• Locating Ruelle-Pollicott resonances
• A semi-invertible operator Oseledets theorem