V. Baladi, S. Isola and B. Schmitt
Transfer operator for piecewise affine approximations of interval maps
(33K, TeX)
ABSTRACT. We consider a natural approximation scheme for piecewise expanding,
piecewise C^(1+Lipschitz), mixing Markov interval maps f
by piecewise affine maps.
We prove that the densities of the absolutely continuous
invariant probability measures of the approximations converge
exponentially fast to the density of the absolutely continuous
invariant probability measure of f in the uniform norm.
To do this we compare the relevant transfer operators of the approximations
with that of f, and use recently developed perturbation techniques.