A semi-classical study of the Casati-Prosen triangle map

We investigate the semi-classical properties of a two-parameter family of piece-wise linear maps on the torus known as the Casati-Prosen or triangle map. This map is weakly chaotic and has zero Lyapunov exponent. A correspondence between classical and quantum observables is established, leading to an appropriate statement regarding equidistribution of eigenfunctions in the semi-classical limit. We then give a full description of our numerical study of the eigenvalues and eigenvectors of this family of maps. For generic choices of parameters the spectral and eigenfunction statistics are seen to follow the predictions of the random matrix theory conjecture. PACS number: 05.45.Mt AMS classification scheme numbers: 81Q50, 81S05 Submitted to: Nonlinearity