Intermittency and regularized Fredholm determinants |
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Authors: | Hans Henrik Rugh |
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Affiliation: | (1) University of Warwick, Coventry CV4 7AL, UK, GB |
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Abstract: | 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
associated Perron-Frobenius operator ℳ has a continuous and residual spectrum contained in the line-segment σ
c
=0,1] and a point spectrum σ
p
which has no points of accumulation outside 0 and 1. Furthermore, points in σ
p
−{0,1} are eigenvalues of finite multiplicity. We construct a regularized Fredholm determinant d(λ) which has a holomorphic extension to λ∈ℂ−σ
c
and can be analytically continued from each side of σ
c
to an open neighborhood of σ
c
−{0,1} (on different Riemann sheets). In ℂ−σ
c
the zero-set of d(λ) is in one-to-one correspondence with the point spectrum of ℳ. Through the conformal transformation the function d∘λ(z) extends to a holomorphic function in a domain which contains the unit disc.
Oblatum 10-X-1996 & 31-I-1998 / Published online: 14 October 1998 |
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Keywords: | |
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