Hyperbolicity properties of multi-modal Collet-Eckmann maps without Schwarzian derivative assumptions

Authors:
Tomasz Nowicki and Sebastian van Strien

Journal:
Trans. Amer. Math. Soc. **321** (1990), 793-810

MSC:
Primary 58F08; Secondary 58F13

MathSciNet review:
994169

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Abstract: In this paper we study the dynamical properties of general maps with quadratic critical points (and not necessarily unimodal). We will show that if such maps satisfy the well-known Collet-Eckmann conditions then one has

(a) hyperbolicity on the set of periodic points;

(b) nonexistence of wandering intervals;

(c) sensitivity on initial conditions; and

(d) exponential decay of branches (intervals of monotonicity) of as

For these results we will not make any assumptions on the Schwarzian derivative . We will also give an estimate of the return-time of points that start near critical points.

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1990-0994169-6

Article copyright:
© Copyright 1990
American Mathematical Society