Explicit examples of resonances for Anosov maps of the torus. (1st January 2023)

• Record Type: Journal Article
• Authors: Pollicott, Mark; Sewell, Benedict
• Is Part Of: Nonlinearity. Volume 36:Number 1(2023)
• Page Start: 110
• Page End: 132
• Publication Date: 2023-01-01
• Subjects: Anosov diffeomorphism -- resonances -- Blaschke product; 37A30 -- 37C05 -- 37D20 -- 37A25; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac9a2e
• Languages: English
• ISSNs: 0951-7715

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.