27 research outputs found
Complete spectral data for analytic Anosov maps of the torus
Using analytic properties of Blaschke factors we construct a family of
analytic hyperbolic diffeomorphisms of the torus for which the spectral
properties of the associated transfer operator acting on a suitable Hilbert
space can be computed explicitly. As a result, we obtain explicit expressions
for the decay of correlations of analytic observables without resorting to any
kind of perturbation argument.Comment: 19 pages, 4 figure
The resonance spectrum of the cusp map in the space of analytic functions
We prove that the Frobenius--Perron operator of the cusp map
, (which is an approximation of the
Poincar\'e section of the Lorenz attractor) has no analytic eigenfunctions
corresponding to eigenvalues different from 0 and 1. We also prove that for any
the spectrum of in the Hardy space in the disk
\{z\in\C:|z-q|<1+q\} is the union of the segment and some finite or
countably infinite set of isolated eigenvalues of finite multiplicity.Comment: Submitted to JMP; The description of the spectrum in some Hardy
spaces is adde