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Subexponential instability in one-dimensional maps implies infinite invariant measure
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10.1063/1.3470091
/content/aip/journal/chaos/20/3/10.1063/1.3470091
http://aip.metastore.ingenta.com/content/aip/journal/chaos/20/3/10.1063/1.3470091
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Probability density function of the normalized Lyapunov exponent of the Pomeau–Manneville map ( and ). The sequence is given by , where and . Solid line represents the probability density function of the normalized Mittag–Leffler distribution of order 2/3.

Image of FIG. 2.
FIG. 2.

Numerical simulations for the growth of the separation in Boole transformation (24). The separations for five different initial points are represented by five dotted lines. The logarithm of the average of and the average of the logarithm of are represented by thick and thin lines, respectively, and the theoretical curve of Eq. (27) is also represented by a line.

Image of FIG. 3.
FIG. 3.

Schematic illustration of and .

Image of FIG. 4.
FIG. 4.

Transformation with a flat critical point at .

Image of FIG. 5.
FIG. 5.

Modified logistic map. Solid and dotted lines represent and , respectively.

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/content/aip/journal/chaos/20/3/10.1063/1.3470091
2010-08-18
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Subexponential instability in one-dimensional maps implies infinite invariant measure
http://aip.metastore.ingenta.com/content/aip/journal/chaos/20/3/10.1063/1.3470091
10.1063/1.3470091
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