2022/09/05 by Cuesta, Javier Echevarría
#37D20 (Secondary) #81Q50 #81S10 (Primary) 37C30 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2209.02027
Faure and Tsujii recently proposed a new quantization theory for symplectic Anosov diffeomorphisms. It combines prequantization with the study of the Pollicott--Ruelle resonances of an associated transfer operator. We apply this framework to the hyperbolic symplectic automorphisms of the 2n-dimensional torus, the so-called cat maps. Our main result gives an explicit relation between the resonances of the prequantum transfer operator and the eigenvalues of the standard quantum cat maps, generalizing the case n=1 previously treated by Faure.