Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Hyperbolicity properties of $ C\sp 2$ 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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study the dynamical properties of general $ {C^2}$ maps $ f:[0,1] \to [0,1]$ 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 $ {f^n}$ as $ n \to \infty ;$

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

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58F08, 58F13

Retrieve articles in all journals with MSC: 58F08, 58F13

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society