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## 2006.99: Hyperbolicity of the invariant set for the logistic map with $\mu > 4$

2006.99: Paul Glendinning (2001) Hyperbolicity of the invariant set for the logistic map with $\mu > 4$. Nonlinear Analysis: Theory, Methods & Applications, 47 (5). pp. 3323-3332. ISSN 0362-546X

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## Abstract

Classic results due to Guckenheimer and Misiurewicz imply that the invariant set of the logistic map with µ in (4,2+\sqrt{5}] is hyperbolic. This is well known, but the only obvious reference in the literature uses relatively sophisticated ideas from complex variable theory. This pedagogical note provides a brief, self-contained account of this result using only elementary real analysis. The method also gives a good estimate of the expansion rate on the invariant set.

Item Type: Article MSC 2000 > 37 Dynamical systems and ergodic theory 2006.99 Professor Paul Glendinning 18 May 2006