Ymele:Circle map poincare recurrence.jpeg
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Scortness
TowritennessCircle map poincare recurrence.jpeg | |
Tælmearc | |
Fruma | https://linas.org/art-gallery/circle-map/circle-map.html |
Dædfruma | User:Linas |
Transferred from en.wikipedia to Commons by Maksim.
Scortness
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.
Scortness
Average Poincaré recurrence time for the circle map. Original artwork created by Linas Vepstas User:Linas <linas@linas.org> 18 January 2006
Leaf:
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.htmlGFDLGNU Free Documentation Licensetruetrue |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | ||
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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> <linas@linas.org>) |
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 <linas@linas.org>)
Items portrayed in this file
depicts English
copyright status English
copyrighted English
inception English
20 Æfterra Geola 2006
media type English
image/jpeg
checksum English
07c6d870b61432e60c7032722116054f9f6bae20
data size English
132,528 Bita
height English
900 pixel
width English
450 pixel
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Dæg/Tid | Metungincel | Micelnesse gemetu | Brucend | Ymbspræc | |
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nu | 18:04, 18 Hreðmonað 2006 | 450 × 900 (129 KB) | Maksim | La 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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