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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
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MIMS number:2006.99
Deposited By:Professor Paul Glendinning
Deposited On:18 May 2006

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