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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