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arXiv · 2104.04608

Nonexistence of spectral gaps in H\"older spaces for continuous time dynamical systems

Ian Melbourne·Nicolo Paviato·Dalia Terhesiu
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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 H\"older space with H\"older exponent greater than 1/2 unless it consists entirely of coboundaries.

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Ian Melbourne, Nicolo Paviato, Dalia Terhesiu. 2021-04-09. Nonexistence of spectral gaps in H\"older spaces for continuous time dynamical systems. https://arxiv.org/abs/2104.04608

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