Explicit examples of resonances for Anosov maps of the torus
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Published:2022-11-18
Issue:1
Volume:36
Page:110-132
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ISSN:0951-7715
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Container-title:Nonlinearity
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language:
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Short-container-title:Nonlinearity
Author:
Pollicott Mark,Sewell Benedict
Abstract
Abstract
In (2017 Nonlinearity
30 2667–86) Slipantschuk, Bandtlow and Just gave concrete examples of Anosov diffeomorphisms of
T
2
for which their resonances could be completely described. Their approach was based on composition operators acting on analytic anisotropic Hilbert spaces. In this note we present a construction of alternative anisotropic Hilbert spaces which helps to simplify parts of their analysis and gives scope for constructing further examples.
Funder
H2020 European Research Council
Engineering and Physical Sciences Research Council
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics