Circle_map_poincare_recurrence.jpeg
Summary
Description Circle map poincare recurrence.jpeg | |
Date | |
Source | https://linas.org/art-gallery/circle-map/circle-map.html |
Author | User:Linas |
Transferred from en.wikipedia to Commons by Maksim .
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 <[email protected]> 18 January 2006
Licensing
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 . http://www.gnu.org/copyleft/fdl.html GFDL GNU Free Documentation License true true |
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This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | |
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This licensing tag was added to this file as part of the GFDL licensing update . http://creativecommons.org/licenses/by-sa/3.0/ CC BY-SA 3.0 Creative Commons Attribution-Share Alike 3.0 true true |
date/time | username | edit summary |
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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> <[email protected]>) |
Original upload log
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- (del) (cur) 04:14, 19 January 2006 . . en:User:Linas Linas ( en:User_talk:Linas Talk) . . 450x900 (132528 bytes) (Histogram of en:Poincaré_recurrence Poincaré recurrence for the en:Circle_map circle map. Original artwork by Linas Vepstas en:User:Linas User:Linas <[email protected]>)