Can I read Prequantum transfer operator for symplectic Anosov diffeomorphism : Frédéric Faure and Masato Tsujii on EtoBox?

Prequantum transfer operator for symplectic Anosov diffeomorphism : Frédéric Faure and Masato Tsujii by Faure, Frédéric; Tsujii, Masato is a nonfiction available to read on EtoBox.

What is Prequantum transfer operator for symplectic Anosov diffeomorphism : Frédéric Faure and Masato Tsujii about?

We define the prequantization of a symplectic Anosov diffeomorphism f:MM as a U(1) extension of the diffeomorphism f preserving a connection related to the symplectic structure on M. We study the spectral properties of the associated transfer operator with a given potential VC^(M), called prequantum transfer operator. This is a model of transfer operators for geodesic flows on negatively curved manifolds (or contact Anosov flows). We restrict the prequantum transfer operator to the N-th Fourier mode with respect to the U(1) action and investigate the spectral property in the limit N, regarding the transfer operator as a Fourier integral operator and using semi-classical analysis. In the main result, under some pinching conditions, we show a ``band structure'' of the spectrum, that is, the spectrum is contained in a few separated annuli and a disk concentric at the origin. We show that, with the special (Hölder continuous) potential V\_0=12|Df|\_E\_u|, where E\_u is the unstable subspace, the outermost annulus is the unit circle and separated from the other parts. For this, we use an extension of the transfer operator to the Grassmanian bundle. Using Atiyah-Bott trace formula, we es

Who reads Prequantum transfer operator for symplectic Anosov diffeomorphism : Frédéric Faure and Masato Tsujii?

Author

Faure, Frédéric; Tsujii, Masato

Publisher

Société mathématique de France

Published

2015

Language

EN

ISBN

9782856298237

Category

nonfiction

Subjects

Mathematics, Stem