Non-leading eigenvalues of the Perron-Frobenius operators for beta-maps

Shintaro Suzuki

We consider the Perron-Frobenius operator defined on the space of functions of bounded variation for the beta-map $\ddot{I}{„}_{\hat{I}}^2(x)={\hat{I}}^{2}x$ (mod $1$), for ${\hat{I}}^2\in (1,\infty )$, and investigate i…