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Nonexistence of spectral gaps in Hölder spaces for continuous time dynamical systems

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Abstract

We show that there is a natural restriction on the smoothness of spaces where the transfer operator for a continuous dynamical system has a spectral gap. Such a space cannot be embedded in a Hölder space with Hölder exponent greater than ½ unless it consists entirely of coboundaries.

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Ian Melbourne & Nicolò Paviato

  2. Mathematisch Instituut, University of Leiden, Niels Bohrweg 1, 2333 CA, Leiden, Netherlands

    Dalia Terhesiu

Authors
  1. Ian Melbourne
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  2. Nicolò Paviato
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  3. Dalia Terhesiu
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Correspondence to Ian Melbourne.

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Melbourne, I., Paviato, N. & Terhesiu, D. Nonexistence of spectral gaps in Hölder spaces for continuous time dynamical systems. Isr. J. Math. 247, 987–991 (2022). https://doi.org/10.1007/s11856-021-2273-3

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  • DOI: https://doi.org/10.1007/s11856-021-2273-3

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