We consider a natural approximation scheme for piecewise expanding, piecewise C1+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 u s e recently developed perturbation techniques.
Transfer operators for piecewise affine approximations of interval maps
ISOLA, Stefano;
1995-01-01
Abstract
We consider a natural approximation scheme for piecewise expanding, piecewise C1+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 u s e recently developed perturbation techniques.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.