File:Henon.jpg

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Log-log plot of \({\hat C}(r,m)\) for the H'enon map versus r, for \(m=1,2,\ldots 8\). The H'enon map is defined as \(x_{i+1} = 1 -1.4x_i^2+0.3y_i,\; y_{i+1} = x_i\). The metric used is the maximum norm. A power law \({\hat C}(r,m) \sim r^D\) with \(D\approx 1.21\) is seem in the central region (\(-10 < \ln r < -2\)) for all curves with \(m\geq 2\). For smaller \(r\), the data look noisy due to lack of statistics. For larger \(r\) one sees deviations from scaling which would be different if the Euclidean norm had been used. The gaps between the curves for \(m\geq 2\) in the scaling region determine the dynamical entropy \(K_2\).

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	23:40, 15 April 2007		431 × 302 (16 KB)	Peter Grassberger (Talk \| contribs)	Log-log plot of <math>{\hat C}(r,m)</math> for the H\'enon map versus r, for <math>m=1,2,\ldots 8</math>. The H\'enon map is defined as <math>x_{i+1} = 1 -1.4x_i^2+0.3y_i,\; y_{i+1} = x_i</math>. The metric used is the maximum norm. A power law <math>{\ha
	23:37, 15 April 2007		431 × 302 (16 KB)	Peter Grassberger (Talk \| contribs)	Log-log plot of <math>{\hat C}(r,m)</math> for the H'enon map versus r, for <math>m=1,2,\ldots 8</math>. The H'enon map is defined as <math>x_{i+1} = 1 -1.4x_i^2+0.3y_i,\; y_{i+1} = x_i</math>. The metric used is the maximum norm. A power law <math>{\hat
	23:30, 15 April 2007		431 × 302 (16 KB)	Peter Grassberger (Talk \| contribs)
	23:25, 15 April 2007		553 × 789 (53 KB)	Peter Grassberger (Talk \| contribs)	Log-log plot of <math>{\hat C}(r,m)</math> for the H{\'e}non map versus r, for <math>m=1,2,\ldots 8</math>. The H{\'e}non map is defined as <math>x_{i+1} = 1 -1.4x_i^2+0.3y_i,\; y_{i+1} = x_i</math>. The metric used is the maximum norm. A power law <math>