Prequantum transfer operator for Anosov diffeomorphism. (Preliminary Version).

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00703234
Contributor : Frédéric Faure <>
Submitted on : Friday, June 1, 2012 - 11:48:32 AM
Last modification on : Thursday, January 11, 2018 - 6:12:13 AM

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  • HAL Id : hal-00703234, version 1
  • ARXIV : 1206.0282

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Frédéric Faure, Masato Tsujii. Prequantum transfer operator for Anosov diffeomorphism. (Preliminary Version).. 2012. ⟨hal-00703234v1⟩

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