Image:Circle map winding number.jpeg

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[edit] Description

This image shows the winding number for the en:circle map. The circle map is defined by the iteration of the map

\theta_{n+1}=\theta_n + \Omega -\frac{K}{2\pi} \sin (2\pi \theta_n).

The winding number is given by considering the asymptotic behavior of the map, that is, by

\omega=\lim_{n\to\infty} \frac{\theta_n}{n}.

In this image, black denotes a winding number of 0, red denotes a winding number of 1, and green denotes a winding number of 0.5. The plot is such that the frequency Ω runs from 0 to 1 along the x-axis, and the coupling constant K runs from 0 at the bottom of the image to 2π at the top.

[edit] Summary

The en:winding number for the en:circle map. Original artwork by Linas Vepstas en:User:Linas <linas@linas.org>, created 18 January 2006.

[edit] Licensing

GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".

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date/time username edit summary
05:48, 19 January 2006 en:User:Linas (add image description)
05:42, 19 January 2006 en:User:Linas (The <a href="/wiki/Winding_number" title="Winding number">winding number</a> for the <a href="/wiki/Circle_map" title="Circle map">circle map</a>. Original artwork by Linas Vepstas <a href="/wiki/User:Linas" title="User:Linas">User:Linas</a> <linas@linas.org>)

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