 96482 Rugh H.H.
 Intermittency and Regularized Fredholm Determinants.
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Oct 8, 96

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Abstract. We consider realanalytic 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 PerronFrobenius operator ${\cal
M}$ has a decomposition $Sp ({\cal M}) = \sigma_c \cup \sigma_p$ where
$\sigma_c=[0,1]$ is the continuous spectrum of ${\cal M}$ 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 zeroset
of $d(\lambda)$ is in onetoone correspondence with the point spectrum of
${\cal M}$. Through the conformal transformation $\lambda(z) = 1/(4z)
(1+z)^2$ the function $d \circ \lambda(z)$ extends to a holomorphic function in
a domain which contains the unit disc.
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