Frédéric Faure, Masato Tsujii
This is a preliminary version and some other results will appear in the next version. We define the prequantization of a symplectic Anosov diffeomorphism, which is a U(1) extension of the diffeomorphism preserving an associated specific connection. We study the spectrum of the associated transfer operator, called prequantum transfer operator, restricted to the N-th Fourier mode with respect to the U(1) action on P. We investigate the spectral property in the limit N to infinity, regarding the transfer operator as a Fourier integral operator and using semi-classical analysis. In the main result, 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.
View original:
http://arxiv.org/abs/1206.0282
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