| H. Thunberg, Unfolding chaotic quadratic maps{parameter dependence of natural measures, preprint 1998, http://www.ima.mdh.se/personal/htg/hat.ps 25 |
.... f k (c) j =0 D 2 f k 0 (c) Df k 0 (a) and where d 0 dm is the Radon Nikodym derivative of 0 , i.e. d 0 dm (c) is the density of 0 at c. Remark 1. 1 Discontinuity of invariant measures of f at = 0 was observed by Tsujii [Tsu96] and Thunberg [Thu98]; their observations imply discontinuity of N at = 0. That a set of parameter values of positive measure exists for which f admits an a.c.i.m. follows from the celebrated work by Jakobson [Jak81] and its extensions. The set is xed in Proposition 5.1 below. Formula (3) says that the ....
H. Thunberg, Unfolding chaotic quadratic maps{parameter dependence of natural measures, preprint 1998, http://www.ima.mdh.se/personal/htg/hat.ps 25
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