1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Boundaries of Siegel disks: Numerical studies of their dynamics and regularity
Rent:
Rent this article for
USD
10.1063/1.2985856
/content/aip/journal/chaos/18/3/10.1063/1.2985856
http://aip.metastore.ingenta.com/content/aip/journal/chaos/18/3/10.1063/1.2985856

Figures

Image of FIG. 1.
FIG. 1.

Critical points and Siegel disks of the map (3) for (∗ and a thin line), (+ and a thick line), and (× and a dotted line).

Image of FIG. 2.
FIG. 2.

Siegel disks of the maps [given by Eq. (4) ] with critical point of order (outermost curve), , and (innermost curve). See text for details.

Image of FIG. 3.
FIG. 3.

Graphs of the real (solid lines) and the imaginary (dashed lines) parts of the map corresponding to of the map (3) for (thin lines) and (thick lines); cf. Fig. 1 .

Image of FIG. 4.
FIG. 4.

Plot of vs for the map (3) with ; see text for details.

Image of FIG. 5.
FIG. 5.

Plot of vs for the map (3) with ; see text for details.

Image of FIG. 6.
FIG. 6.

Plot of vs for the map (3) with (top), (bottom); see text for details.

Image of FIG. 7.
FIG. 7.

Plot of vs for the maps with .

Image of FIG. 8.
FIG. 8.

(Top) plot of vs for the map (3) with . (Bottom) plot of the differences between the vertical coordinates of adjacent points in the top figure.

Image of FIG. 9.
FIG. 9.

(Top) plot of vs for the map (3) with . (Bottom) plot of the differences between the vertical coordinates of adjacent points in the top figure.

Image of FIG. 10.
FIG. 10.

Plot of the phases of the Fourier coefficients (vs ) of for the map .

Image of FIG. 11.
FIG. 11.

Histogram of some of the phases shown in Fig. 10 (from ).

Image of FIG. 12.
FIG. 12.

Kolmogorov-Smirnov test for normality of the phases in .

Image of FIG. 13.
FIG. 13.

Plot of vs for rotation numbers (circles), (squares), (diamonds), (triangles), and (pluses).

Tables

Generic image for table
Table I.

Global Hölder regularity for maps with rotation numbers , and critical point of order .

Generic image for table
Table II.

Values of for maps of the form [Eq. (4) ] with different rotation numbers and orders of the critical point.

Generic image for table
Table III.

Areas of the Siegel disks for maps of the form [see Eq. (4) ] with different rotation numbers and orders of the critical point.

Generic image for table
Table IV.

Upper bounds on the Hölder regularity [Eq. (16) ] for maps of the form [Eq. (4) ] with rotation numbers and critical point of order .

Loading

Article metrics loading...

/content/aip/journal/chaos/18/3/10.1063/1.2985856
2008-09-29
2014-04-18
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Boundaries of Siegel disks: Numerical studies of their dynamics and regularity
http://aip.metastore.ingenta.com/content/aip/journal/chaos/18/3/10.1063/1.2985856
10.1063/1.2985856
SEARCH_EXPAND_ITEM