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File:Circle map poincare recurrence.jpeg

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Description
English: en:Arnold tongues found in the en:circle map.
Date
Source https://linas.org/art-gallery/circle-map/circle-map.html
Author User:Linas

Transferred from en.wikipedia to Commons by Maksim.

The original description page was here. All following user names refer to en.wikipedia.

Summary

The circle map is a chaotic map showing a number of interesting chaotic behaviors.

This figure shows the average Poincaré recurrence time for the iterated circle map modulo 1. The circle map is given by iterating on the map

Given a fixed value of K, Ω, and ε, the recurrence time N is given by the smallest integer N such that

is satisfied. This figure shows the average values of N for a variety of random starting values , and an ε = 0.0001. Black indicates values of N of less than about 10, blue values of about 50, green shows values of about 140 and red shows values greater than 250.

The frequency Ω runs from 0 to 1 along the horizontal axis, and the coupling constant K runs from 0 at the bottom to 4π at the top of the image. The upper limit of the red area at the bottom occurs at K=1.

Summary

Average Poincaré recurrence time for the circle map. Original artwork created by Linas Vepstas User:Linas <linas@linas.org> 18 January 2006

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.
w:en:Creative Commons
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date/time username edit summary
05:21, 19 January 2006 en:User:Linas (error in description)
04:41, 19 January 2006 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Circle_map_poincare_recurrence.jpeg#Description" title="Image:Circle map poincare recurrence.jpeg">→</a>Description -</span> Note)
04:35, 19 January 2006 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Circle_map_poincare_recurrence.jpeg#Description" title="Image:Circle map poincare recurrence.jpeg">→</a>Description</span>)
04:25, 19 January 2006 en:User:Linas (start adding sdescription)
04:14, 19 January 2006 en:User:Linas (Histogram of <a href="/wiki/Poincar%C3%A9_recurrence" title="Poincaré recurrence">Poincaré recurrence</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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Date/TimeThumbnailDimensionsUserComment
current18:04, 18 March 2006Thumbnail for version as of 18:04, 18 March 2006450 × 900 (129 KB)MaksimLa bildo estas kopiita de wikipedia:en. La originala priskribo estas: == Description == This figure shows the average Poincaré recurrence time for the iterated circle map modulo 1. The circle map is given by iterating on the map :<math>\theta

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