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Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems
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10.1063/1.3697985
/content/aip/journal/chaos/22/2/10.1063/1.3697985
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/2/10.1063/1.3697985
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The rectangular billiard, with dimension , has four rounded corners (with radius R, see magnification of just one border). The escape point with aperture a lies exactly in the middle of the billiard. Initial angle and, schematically, the shortest escape trajectories ( , and ) are shown. In all simulations, we use L = 4 and D = 10.

Image of FIG. 2.
FIG. 2.

Phase-space dynamics for (a) R = 0 and (b) R/L = 0.1 (one IC): Green (light gray) points occur when the trajectory collides with the rounded corner and defines the SR or chaotic region. Blue (dark gray) points occur when the trajectory collides with the vertical and horizontal parallel walls.

Image of FIG. 3.
FIG. 3.

(a) Escape angle as a function of and , (b) and (c) are magnifications.

Image of FIG. 4.
FIG. 4.

Semi-log plot of for distinct values of R/L. Each curve was obtained using ICs.

Image of FIG. 5.
FIG. 5.

Grid of points with the FTLEs as a function of .

Image of FIG. 6.
FIG. 6.

FTLEs in the phase space projection for K = 0.15 [see white dashed line in Fig. 5(a) ].

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/content/aip/journal/chaos/22/2/10.1063/1.3697985
2012-06-21
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/2/10.1063/1.3697985
10.1063/1.3697985
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