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Numerical estimates of local dimension by waiting time and quantitative recurrence

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Academic year: 2021

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Figure

Fig. 1. Baker map. On the top parameters are: l 1 ¼ l 2 ¼ 1=3, c 1 ¼ 0:51 and c 2 ¼ 0:512211122, whereas on the bottom l 1 ¼ l 2 ¼ p 1 ffiffi 5 , c 1 ¼ 0:51 and c 2 ¼ 0:512211122
Fig. 3. On the top slanted Baker map with parameters l 1 ¼ l 2 ¼ p 1 ffiffi 5 , m 1 ¼ 1 6 , m 2 ¼ 0, c 1 ¼ 0:3, c 2 ¼ 0:512211122, whereas on the bottom non-linear slanted Baker map with same parameters as slanted Baker map and ¼ 0:01
Fig. 5. He´non map with parameters a ¼ 1:2, b ¼ 0:2. On the top recurrence vs dimension, thin line is logðt r ðy; yÞÞ= logðrÞ, thick line is hR r ðyÞi with the mean over 200 different initial points x k , and horizontal dashed line is the dimension comput
Fig. 6. Translation by the angle y ¼ 0:50050000005000000000005. Thin line is logðt r ðy; yÞÞ= logðrÞ, thick line is hR r ðyÞi with the mean over 10 different initial points x k , and the horizontal dashed line with ordinate 1 is the theoretical dimension.

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