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Subexponential instability in one-dimensional maps implies infinite invariant measure
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10.1063/1.3470091
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Affiliations:
1 Department of Applied Physics, Advanced School of Science and Engineering, Waseda University, Okubo 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan
a) Electronic mail: akimoto@z8.keio.jp.
Chaos 20, 033110 (2010)
/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

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.

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.

FIG. 3.

Schematic illustration of and .

FIG. 4.

Transformation with a flat critical point at .

FIG. 5.

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

/content/aip/journal/chaos/20/3/10.1063/1.3470091
2010-08-18
2014-04-17

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