Spectra of expanding maps on Besov spaces

Yushi Nakano; Shota Sakamoto

doi:10.3934/dcds.2019077

Article Contents

2019, Volume 39, Issue 4: 1779-1797. Doi: 10.3934/dcds.2019077

This issue Previous Article Vortex structures for some geometric flows from pseudo-Euclidean spaces Next Article Linear response for Dirac observables of Anosov diffeomorphisms

Spectra of expanding maps on Besov spaces

Yushi Nakano^1, and
Shota Sakamoto^2,

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: September 30, 2017

Revised: August 31, 2018

Published: January 2019

This work was partially supported by JSPS KAKENHI Grant Numbers 16J03963 and 17K05283

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Abstract

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.

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Mathematics Subject Classification: Primary: 37C30; Secondary: 37D20.

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