## 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 |
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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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