Another proof of Jakobson's Theorem and related results
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The author shows that any family C 2-close to f a (x) = 1 − ax 2 (2 − e ≤ a ≤ 2) satisfies Jakobson’s theorem: For a positive measure set of a the transformation f a has an absolutely continuous invariant measure. He also indicates some generalizations.
[1] Lennart Carleson,et al. On Iterations of 1 - ax 2 on (- 1,1) , 1985 .
[2] Marek R Rychlik,et al. Bounded variation and invariant measures , 1983 .
[3] Michał Misiurewicz,et al. Absolutely continuous measures for certain maps of an interval , 1981 .
[4] M. Jakobson. Absolutely continuous invariant measures for one-parameter families of one-dimensional maps , 1981 .
[5] Mary Rees,et al. Positive measure sets of ergodic rational maps , 1986 .