94-277 V. Baladi, S. Isola and B. Schmitt

Transfer operator for piecewise affine approximations of interval maps (33K, TeX) Sep 2, 94

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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.

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