Image:Devils-staircase.svg

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[edit] Description

This figure shows the winding number for the circle map, as a function of Ω, with K held constant, at K=1. It is an example of the Devil's staircase. Each of the flat regions corresponds to a region of phase-locking; that is, each flat area is a slice through one of the Arnold tongues.

The circle map is a model of the phase-locked loop, and is given by iterating the equation

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

The winding number is defined as the limiting behavior of the system after many iterations, by:

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

This graph shows ω on the vertical axis as a function of Ω on the horizontal axis.

[edit] Image history

Original image created by Linas Vepstas User:Linas on 17 January 2006.

date/time username edit summary
15:37, 17 January 2006 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Devils-staircase.svg#Description" title="Image:Devils-staircase.svg">→</a>Description -</span> further details)
15:22, 17 January 2006 en:User:Linas (Provide description of the image)
15:15, 17 January 2006 en:User:Linas (Original image created by Linas Vepstas <a href="/wiki/User:Linas" title="User:Linas">User:Linas</a> 17 January 2006)

[edit] Historio de la dosiero

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[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/TimeDimensionsUserComment
current18:05, 18 March 2006600×480 (10 KB)Maksim (La bildo estas kopiita de wikipedia:en. La originala priskribo estas: == Description == This figure shows the winding number for the circle map, as a function of &Omega;, with ''K'' held constant, at ''K''=1. It is an example of the [[Devil's sta)
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