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Bounded recurrence of critical points and Jakobson’s theorem. (English) Zbl 1062.37027
Lei, Tan, The Mandelbrot set, theme and variations. Cambridge: Cambridge University Press (ISBN 0-521-77476-4/pbk). Lond. Math. Soc. Lect. Note Ser. 274, 173-210 (2000).
Summary: We prove that the set of quadratic interval maps which satisfy a strong bounded recurrence condition on the orbit of the critical point has positive Lebesgue measure. This implies classical teorems of M. V. Jakobson [Commun. Math. Phys. 81, 39–88 (1981; Zbl 0497.58017)] and Benedicks-Carleson.
For the entire collection see [Zbl 0935.00019].

MSC:
37E05 Dynamical systems involving maps of the interval
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