# American Institute of Mathematical Sciences

April  2019, 39(4): 1779-1797. doi: 10.3934/dcds.2019077

## Spectra of expanding maps on Besov spaces

 1 Kitami Institute of Technology, Faculty of Engineering, 165 Koen-cho, Kitami, Hokkaido, 090-8507, Japan 2 Kyoto University, Graduate School of Human and Environmental Studies, Yoshida Nihonmatsu-cho, Sakyo-ku, Kyoto, 606-8501, Japan

Received  October 2017 Revised  September 2018 Published  January 2019

Fund Project: This work was partially supported by JSPS KAKENHI Grant Numbers 16J03963 and 17K05283.

A typical approach to analysing statistical properties of expanding maps is to show spectral gaps of associated transfer operators in adapted function spaces. The classical function spaces for this purpose are Hölder spaces and Sobolev spaces. Natural generalisations of these spaces are Besov spaces, on which we show a spectral gap of transfer operators.

Citation: Yushi Nakano, Shota Sakamoto. Spectra of expanding maps on Besov spaces. Discrete & Continuous Dynamical Systems, 2019, 39 (4) : 1779-1797. doi: 10.3934/dcds.2019077
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