Image:Circle map poincare recurrence.jpeg
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[edit] 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
Given a fixed value of K, Ω, θn and ε, the recurrence time N is given by the smallest integer N such that
is satisfied. This figure shows the average value of N for a variety of starting values θn, and an ε = 0.003. 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.
[edit] Summary
Average Poincaré recurrence time for the circle map. Original artwork created by Linas Vepstas User:Linas <linas@linas.org> 18 January 2006
[edit] Licensing
| 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>) |
[edit] Historio de la dosiero
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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>)
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| Date/Time | Dimensions | User | Comment | |
|---|---|---|---|---|
| current | 18:04, 18 March 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) |
