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The experimental localization of Aubry–Mather sets using regularization techniques inspired by viscosity theory
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10.1063/1.2756264
/content/aip/journal/chaos/17/3/10.1063/1.2756264
http://aip.metastore.ingenta.com/content/aip/journal/chaos/17/3/10.1063/1.2756264
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Numerical computation of for the preliminary steps, using both the norm (upper curve) and the norm (lower curve). In both cases, the minimum value of is obtained for .

Image of FIG. 2.
FIG. 2.

On the left: we report the numerical computation of for different values of . The minimum is found for . On the right: numerical computation of (continuous line) and (dashed line) versus , obtained for . The norm is reduced up to order for , and after this value the precision of the numerical computation evidently affects the computations.

Image of FIG. 3.
FIG. 3.

On the top we represent vs ; on the middle we represent (part of the plot of) vs . The density of the points indicate that a good value for is , which corresponds to the limit distance of . On the bottom: representation in the phase–space of the 42 204 approximate points of the cantorus that satisfy (30).

Image of FIG. 4.
FIG. 4.

On the top: representation in the phase-space of 1 947 069 approximate points of the cantorus. On the bottom: zoom of the 1 947 069 points of the cantorus and a zoom of the 42 204 points shifted of in the action coordinate (to compare the two sets). It is evident a very good correspondence of the two sets, with no significant enlargements of the part of the cantorus passing from the original set to the one obtained with 100 iterations.

Image of FIG. 5.
FIG. 5.

On the top: representation in the phase–space of a set of 1 622 521 approximate points of the cantorus. On the bottom: zoom of the 1 622 521 points of the cantorus and a zoom of the 54 305 points shifted of in the action coordinate (to compare the two sets). It is evident a very good correspondence of the two sets, with no significant enlargements of the part of the cantorus passing from the original set to the one obtained with 100 iterations.

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/content/aip/journal/chaos/17/3/10.1063/1.2756264
2007-08-17
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The experimental localization of Aubry–Mather sets using regularization techniques inspired by viscosity theory
http://aip.metastore.ingenta.com/content/aip/journal/chaos/17/3/10.1063/1.2756264
10.1063/1.2756264
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