Thomas Prellberg
Complete Determination of the Spectrum of a Transfer Operator associated with Intermittency
(99K, gzipped tar file)

ABSTRACT.  It is well established that the physical phenomenon of intermittency can be investigated via the spectral analysis of a 
transfer operator associated with the dynamics of an interval map with indifferent fixed point. We present here for the 
first time a complete spectral analysis for an example of such an intermittent map, the Farey map. We give a simple proof 
that the transfer operator is self-adjoint on a suitably defined Hilbert space and show that its spectrum decomposes into 
a continuous part (the interval $[0,1]$) and isolated eigenvalues of finite multiplicity. Using a suitable first-return map, 
we present a highly efficient numerical method for the determination of all the eigenvalues, including the ones embedded in 
the continuous spectrum.