For almost every tent map, the turning point is typical

Bruin, Henk

Bruin, Henk

Fundamenta Mathematicae, Tome 158 (1998), p. 215-235 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $T_{a}$ be the tent map with slope a. Let c be its turning point, and $μ_{a}$ the absolutely continuous invariant probability measure. For an arbitrary, bounded, almost everywhere continuous function g, it is shown that for almost every a, $ʃ g d μ_{a} = l i m_{n \to \infty} \frac{1}{n} \sum_{i = 0}^{n - 1} g (T_{a}^{i} (c))$ . As a corollary, we deduce that the critical point of a quadratic map is generically not typical for its absolutely continuous invariant probability measure, if it exists.

Publié le : 1998-01-01

Zbl 0962.37015

EUDML-ID : urn:eudml:doc:212253

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     author = {Henk Bruin},
     title = {For almost every tent map, the turning point is typical},
     journal = {Fundamenta Mathematicae},
     volume = {158},
     year = {1998},
     pages = {215-235},
     zbl = {0962.37015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv155i3p215bwm}
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Bruin, Henk. For almost every tent map, the turning point is typical. Fundamenta Mathematicae, Tome 158 (1998) pp. 215-235. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv155i3p215bwm/

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