Intermittency and Regularized Fredholm Determinants

We consider real-analytic maps of the interval $I=[0,1]$ which are expanding everywhere except for a neutral fixed point at 0. We show that on a certain function space the spectrum of the associated Perron-Frobenius operator ${\cal M}$hasadecomposition$Sp ({\cal M}) = \sigma_c \cup \sigma_p$where$\sigma_c=[0,1]$isthecontinuousspectrumof${\cal M}$and$\sigma_p$ is the pure point spectrum with no points of accumulation outside 0 and 1. We construct a regularized Fredholm determinant $d(\lambda )$ which has a holomorphic extension to $\lambda \in C-{\sigma }_c$ and can be analytically continued from each side of ${\sigma }_c$ to an open neighborhood of ${\sigma }_c-0,1$ (on different Riemann sheets). In $C-{\sigma }_c$ the zero-set of $d(\lambda )$ is in one-to-one correspondence with the point spectrum of ${\cal M}$\mathrm{.}Throughtheconformaltransformation$\lambda(z) = 1/(4z) (1+z)^2$ the function $d\circ \lambda (z)$ extends to a holomorphic function in a domain which contains the unit disc.